Central limit theorem for linear eigenvalue statistics of elliptic random matrices

TL;DR

This paper proves a central limit theorem for linear eigenvalue statistics of elliptic random matrices, extending classical results to a broader class of matrices with real entries.

Contribution

It establishes a CLT for elliptic random matrices with analytic test functions, generalizing previous results to real iid matrices.

Findings

CLT holds for linear eigenvalue statistics of elliptic matrices

Results extend to real iid matrices

Generalizes classical ensembles in random matrix theory

Abstract

We consider a class of elliptic random matrices which generalize two classical ensembles from random matrix theory: Wigner matrices and random matrices with iid entries. In particular, we establish a central limit theorem for linear eigenvalue statistics of real elliptic random matrices under the assumption that the test functions are analytic. As a corollary, we extend the results of Rider and Silverstein to real iid random matrices.