A note on the Marchenko-Pastur law for a class of random matrices with dependent entries

TL;DR

This paper demonstrates that for a specific class of real random matrices with dependent entries, the empirical spectral distribution converges to the Marchenko-Pastur law, and provides a rate of convergence.

Contribution

It extends the Marchenko-Pastur law to matrices with dependent entries and quantifies the convergence rate of the spectral distribution.

Findings

Empirical spectral distribution converges to Marchenko-Pastur law.

Provides a rate of convergence for the spectral distribution.

Applicable to matrices with dependent entries.

Abstract

We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical spectral distribution.