2000 character limit reached
Correlation functions between singular values and eigenvalues (2403.19157v4)
Published 28 Mar 2024 in math.PR, math-ph, math.MP, math.ST, and stat.TH
Abstract: Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size, we aim at finding the induced probability measure on $j$ eigenvalues and $k$ singular values that we coin $j,k$-point correlation measure. We find an expression for the $1,k$-point correlation measure which simplifies drastically when assuming that the singular values follow a polynomial ensemble, yielding a closed formula in terms of the kernel corresponding to the determinantal point process of the singular value statistics. These expressions simplify even further when the singular values are drawn from a P\'{o}lya ensemble and extend known results between the eigenvalue and singular value statistics of the corresponding bi-unitarily invariant ensemble.
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Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Burda, Z., Kieburg, M., Nagao, T.: Universal microscopic correlation functions for products of truncated unitary matrices. Journal of Physics A: Mathematical and Theoretical 47(25), 255202 (2014) https://doi.org/10.1088/1751-8113/47/25/255202 arXiv:1310.6395 Ameur et al. [2023] Ameur, Y., Charlier, C., Moreillon, P.: Eigenvalues of truncated unitary matrices: disk counting statistics (2023) arXiv:2305.08976 [math-ph] Anderson et al. [2010] Anderson, G., Guionnet, A., Zeitouni, O.: An Introduction to Random Matrices. Cambridge studies in advanced mathematics 118. Cambridge university press, Cambridge (2010) Akemann and Ipsen [2015] Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ameur, Y., Charlier, C., Moreillon, P.: Eigenvalues of truncated unitary matrices: disk counting statistics (2023) arXiv:2305.08976 [math-ph] Anderson et al. [2010] Anderson, G., Guionnet, A., Zeitouni, O.: An Introduction to Random Matrices. Cambridge studies in advanced mathematics 118. Cambridge university press, Cambridge (2010) Akemann and Ipsen [2015] Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Anderson, G., Guionnet, A., Zeitouni, O.: An Introduction to Random Matrices. Cambridge studies in advanced mathematics 118. Cambridge university press, Cambridge (2010) Akemann and Ipsen [2015] Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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[2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. 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[2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. 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[2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. 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Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. 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Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. 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[2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. 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Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Anderson, G., Guionnet, A., Zeitouni, O.: An Introduction to Random Matrices. Cambridge studies in advanced mathematics 118. Cambridge university press, Cambridge (2010) Akemann and Ipsen [2015] Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Ipsen, J.R.: Recent exact and asymptotic results for products of independent random matrices. Acta Physica Polonica B 46(9), 1747 (2015) https://doi.org/10.5506/aphyspolb.46.1747 arXiv:1502.01667 Akemann et al. [2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. 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[2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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[2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. 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Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. 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Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2013] Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Ipsen, J.R., Kieburg, M.: Products of rectangular random matrices: Singular values and progressive scattering. Physical Review E 88(5) (2013) https://doi.org/10.1103/physreve.88.052118 arXiv:1307.7560 Akemann et al. [2013] Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. 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[2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). 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Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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[2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. 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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. 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[2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Akemann, G., Kieburg, M., Wei, L.: Singular value correlation functions for products of Wishart random matrices. Journal of Physics A: Mathematical and Theoretical 46(27), 275205 (2013) https://doi.org/10.1088/1751-8113/46/27/275205 arXiv:1303.5694 Andreev [1886] Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. 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Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). 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Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Andreev, K.A.: Note sur une relation entre les intégrales définies des produits des fonctions. Mémoires de la Societé des Sciences physiques et naturelles de Bordeaux (1886) Byun and Forrester [2023a] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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[2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. 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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. 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[2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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[2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. 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Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. 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Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. 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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles I: GinUE (2023) arXiv:2211.16223 [math-ph] Byun and Forrester [2023b] Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Byun, S.-S., Forrester, P.J.: Progress on the study of the Ginibre ensembles II: GinOE and GinSE (2023) arXiv:2301.05022 [math-ph] Bardenet et al. [2021] Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. 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Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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[2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. 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Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bardenet, R., Ghosh, S., Lin, M.: Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD. Advances in Neural Information Processing Systems, 16226–16237 (2021) https://doi.org/10.48550/arXiv.2112.06007 arXiv:2112.06007 [stat.ML] Bianchi et al. [2021] Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bianchi, E., Hackl, L., Kieburg, M.: Page curve for fermionic Gaussian states. Physical Review B 103(24) (2021) https://doi.org/10.1103/physrevb.103.l241118 arXiv:2103.05416 Braun et al. [2022] Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. 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[2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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[2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Braun, P., Hahn, N., Waltner, D., Gat, O., Guhr, T.: Winding number statistics of a parametric chiral unitary random matrix ensemble. Journal of Physics A Mathematical General 55(22), 224011 (2022) https://doi.org/10.1088/1751-8121/ac66a9 arXiv:2112.14575 [math-ph] Bhosale et al. [2018] Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Bhosale, U.T., Tekur, S.H., Santhanam, M.S.: Scaling in the eigenvalue fluctuations of correlation matrices. Phys. Rev. E 98, 052133 (2018) https://doi.org/10.1103/PhysRevE.98.052133 arXiv:1807.07968 Deift and Gioev [2009] Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. 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Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. 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[2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Deift, P., Gioev, D.: Random Matrix Theory: Invariant Ensembles and Universality. Courant Lecture Notes. American Mathematical Soc., New York (2009) Duistermaat and Kolk [2010] Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Duistermaat, J.J., Kolk, J.A.C.: Distributions: Theory and Applications, 1st edn. Cornerstones. Birkhäuser Boston, Boston, MA (2010) Dyson [1962] Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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[2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Dyson, F.J.: Statistical theory of the energy levels of complex systems. III. Journal of Mathematical Physics 3(1), 166–175 (1962) https://doi.org/10.1063/1.1703775 Forrester et al. [2018] Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. 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Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J., Ipsen, J.R., Liu, D.-Z.: Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral. Annales Henri Poincaré 19, 1307–1348 (2018) https://doi.org/10.1007/s00023-018-0654-x arXiv:1702.07100 Förster et al. [2020] Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Förster, Y.-P., Kieburg, M., Kösters, H.: Polynomial ensembles and Pólya frequency functions. Journal of Theoretical Probability 34(4), 1917–1950 (2020) https://doi.org/10.1007/s10959-020-01030-z arXiv:1710.08794 Forrester [2010] Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. 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[2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Forrester, P.J.: Log-Gases and Random Matrices (LMS-34). Princeton University Press, Princeton (2010). https://doi.org/10.1515/9781400835416 Feinberg and Zee [1997a] Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism. Nuclear Physics B 501(3), 643–669 (1997) https://doi.org/10.1016/s0550-3213(97)00419-7 arXiv:cond-mat/9704191 Feinberg and Zee [1997b] Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. 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Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Feinberg, J., Zee, A.: Non-Hermitian random matrix theory: Method of Hermitian reduction. Nuclear Physics B 504(3), 579–608 (1997) https://doi.org/10.1016/s0550-3213(97)00502-6 arXiv:cond-mat/9703087 Ghosh [2015] Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ghosh, S.: Determinantal processes and completeness of random exponentials: the critical case. Probab. Theory Relat. Fields 163, 643–665 (2015) https://doi.org/10.48550/arXiv.1211.2435 arXiv:1211.2435 [math.PR] Guionnet et al. [2009] Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. 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Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. 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Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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[2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Guionnet, A., Krishnapur, M., Zeitouni, O.: The single ring theorem. Annals of Mathematics 174, 1189–1217 (2009) https://doi.org/10.4007/annals.2011.174.2.10 arXiv:0909.2214v2 Hahn et al. [2023a] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence. Journal of Mathematical Physics 64(2), 021901 (2023) https://doi.org/10.1063/5.0112423 arXiv:2207.08612 [math-ph] Hahn et al. [2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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[2023b] Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Hahn, N., Kieburg, M., Gat, O., Guhr, T.: Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case. Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. 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Journal of Mathematical Physics 64(11), 111902 (2023) https://doi.org/10.1063/5.0164352 arXiv:2306.12051 [math-ph] Haagerup and Larsen [2000] Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. 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The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Haagerup, U., Larsen, F.: Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras. Journal of Functional Analysis 176(2), 331–367 (2000) https://doi.org/10.1006/jfan.2000.3610 Ho and Zhong [2023] Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. 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Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ho, C.-W., Zhong, P.: Deformed single ring theorems (2023) arXiv:2210.11147 [math.PR] Ipsen [2015] Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. 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Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Ipsen, J.R.: Products of independent Gaussian random matrices (2015) arXiv:1510.06128 [math-ph] Kieburg [2022] Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Kieburg, M.: Hard edge statistics of products of Pólya ensembles and shifted GUE’s. Journal of Approximation Theory 276, 105704 (2022) https://doi.org/10.1016/j.jat.2022.105704 arXiv:1909.04593v4 Kieburg and Kösters [2016] Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Kieburg, M., Kösters, H.: Exact relation between singular value and eigenvalue statistics. Random Matrices: Theory and Applications 05(04), 1650015 (2016) https://doi.org/10.1142/s2010326316500155 arXiv:1601.02586 Kieburg and Kösters [2019] Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kösters, H.: Products of random matrices from polynomial ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55(1) (2019) https://doi.org/10.1214/17-aihp877 arXiv:1601.03724 Kieburg et al. [2015] Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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[2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Kieburg, M., Kuijlaars, A.B.J., Stivigny, D.: Singular value statistics of matrix products with truncated unitary matrices. International Mathematics Research Notices 2016(11), 3392–3424 (2015) https://doi.org/10.1093/imrn/rnv242 arXiv:1501.03910 Kuijlaars and Stivigny [2014] Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Kuijlaars, A.B.J., Stivigny, D.: Singular values of products of random matrices and polynomial ensembles. Random Matrices: Theory and Applications 03(03), 1450011 (2014) https://doi.org/10.1142/S2010326314500117 arXiv:0909.2214 Kuijlaars [2016] Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. 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Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J.: Transformations of Polynomial Ensembles. In: Modern Trends in Constructive Function Theory, vol. 661, pp. 253–268 (2016). https://doi.org/10.1090/conm/661 . https://arxiv.org/abs/1501.05506 Kanazawa et al. [2011] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator in dense QCD-like theories. JHEP 12, 007 (2011) https://doi.org/10.1007/JHEP12(2011)007 arXiv:1110.5858 [hep-ph] Kanazawa et al. [2012] Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. 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Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. 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In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. 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Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. 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Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kanazawa, T., Wettig, T., Yamamoto, N.: Singular values of the Dirac operator at nonzero density. PoS LATTICE2012, 087 (2012) https://doi.org/10.22323/1.164.0087 arXiv:1212.2141 [hep-lat] Kuijlaars and Zhang [2014] Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Kuijlaars, A.B.J., Zhang, L.: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits. Communications in Mathematical Physics 332(2), 759–781 (2014) https://doi.org/10.1007/s00220-014-2064-3 arXiv:1308.1003 Kieburg and Zhang [2023] Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Kieburg, M., Zhang, J.: Derivative principles for invariant ensembles. Advances in Mathematics 413, 108833 (2023) https://doi.org/10.1016/j.aim.2022.108833 arXiv:2007.15259v2 Long et al. [2023] Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Long, Z., Li, Z., Lin, R., Qiu, J.: On singular values of large dimensional lag-τ𝜏\tauitalic_τ sample auto-correlation matrices. Journal of Multivariate Analysis 197, 105205 (2023) https://doi.org/10.1016/j.jmva.2023.105205 arXiv:2202.12526 Lal Mehta [2004] Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Lal Mehta, M.: Random Matrices, 3rd edn. Pure and applied mathematics series, vol. 142. Elsevier Science and Technology, San Diego (2004) Loubaton and Mestre [2021] Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Loubaton, P., Mestre, X.: Testing uncorrelation of multi-antenna signals using linear spectral statistics of the spatio-temporal sample autocorrelation matrix. In: 2021 IEEE Statistical Signal Processing Workshop (SSP), pp. 201–205 (2021). https://doi.org/10.1109/SSP49050.2021.9513815 Narayanan et al. [2023] Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Narayanan, H., Sheffield, S., Tao, T.: Sums of GUE matrices and concentration of hives from correlation decay of eigengaps (2023) arXiv:2306.11514 [math.PR] Nowak and Tarnowski [2017] Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Nowak, M.A., Tarnowski, W.: Spectra of large time-lagged correlation matrices from random matrix theory. Journal of Statistical Mechanics: Theory and Experiment 2017(6), 063405 (2017) https://doi.org/10.1088/1742-5468/aa6504 arXiv:1612.06552 Rudelson and Vershynin [2014] Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Rudelson, M., Vershynin, R.: Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society 27(2), 293–338 (2014) https://doi.org/10.1090/S0894-0347-2013-00771-7 arXiv:1206.5180 Schwartz [1966] Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Schwartz, L.: Théorie des Distributions., 2nd edn. Publications de l’Institut de mathématique de l’Université de Strasbourg 9-10. Hermann, Paris (1966) Soshnikov [2002] Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Soshnikov, A.: Gaussian limit for determinantal random point fields. Ann. Probab. 30, 171–187 (2002) https://doi.org/10.48550/arXiv.math/0006037 arXiv:math/0006037 [math.PR] Thurner and Biely [2007] Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Thurner, S., Biely, C.: The eigenvalue spectrum of lagged correlation matrices. Acta Physica Polonica B 38, 4111–4122 (2007) Weyl [1949] Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Weyl, H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proceedings of the National Academy of Sciences of the United States of America 35(7), 408–411 (1949) Yao and Yuan [2022] Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165 Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
- Yao, J., Yuan, W.: On eigenvalue distributions of large autocovariance matrices. The Annals of Applied Probability 32(5), 3450–3491 (2022) https://doi.org/10.1214/21-AAP1764 arXiv:2011.09165
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