Central Limit Theorem for Linear Eigenvalue Statistics of Elliptic Random Matrices

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 (Ann Probab 34(6):2118–2143, 2006) to real iid random matrices.