Large deviation theorem for random covariance matrices

TL;DR

This paper proves a large deviation theorem for the spectral distribution of random covariance matrices with independent entries, and explores new properties of Laguerre polynomials relevant to this context.

Contribution

It introduces a large deviation result for empirical spectral distributions of covariance matrices with controlled moments and provides novel properties of Laguerre polynomials.

Findings

Established a large deviation theorem for spectral distributions.

Derived new properties of Laguerre polynomials.

Applicable to covariance matrices with independent entries.

Abstract

We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of Laguerre polynomials are also given.