Effect of correlations in the diagonal matrix A on universality

Determine whether the (super)universal scaling of the level compressibility in the intermediate fractal phase persists when the diagonal matrix A has correlated (non-i.i.d.) entries, rather than independent and identically distributed entries, thereby testing universality under correlated on-site energies.

Background

This work shows that introducing correlations among the off-diagonal elements via a Wishart matrix B preserves the conjectured universality of the level compressibility in the fractal phase, extending results beyond fully uncorrelated ensembles.

The authors point out that correlating the diagonal entries A is a natural next step to test whether the same universality persists when the on-site energies are no longer independent.

References

Finally, several open questions emerge from our study. Since correlations between the entries of B preserve the conjectured universality of the level compressibility, it would be interesting to explore what happens when correlations are also introduced among the entries of A.

— The Wishart--Rosenzweig--Porter random matrix ensemble (2510.15764 - Delapalme et al., 17 Oct 2025) in Section 7 (Conclusions)