Concentration of the spectral measure of large Wishart matrices with dependent entries

TL;DR

This paper develops concentration inequalities for the spectral measure of large Wishart matrices with dependent entries, extending understanding of spectral behavior in complex random matrix models.

Contribution

It introduces new concentration inequalities for spectral measures of Wishart matrices with dependence, broadening applicability beyond independent entries.

Findings

Spectral measure concentrates around its expectation even with dependent entries.

Results apply to empirical covariance matrices in high-dimensional settings.

Provides theoretical bounds for spectral deviations in dependent matrix models.

Abstract

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.