On The Eigenvalue Rigidity of the Jacobi Unitary Ensemble

Abstract: In this paper, we prove an optimal global rigidity estimate for the eigenvalues of the Jacobi unitary ensemble. Our approach begins by constructing a random measure defined through the eigenvalue counting function. We then prove its convergence to a Gaussian multiplicative chaos measure, which leads to the desired rigidity result. To establish this convergence, we apply a sufficient condition from Claeys et al. \cite{CFL2021} and conduct an asymptotic analysis of the related exponential moments.