Limit theorems for spectra of random matrices with martingale structure

Götze F, Tikhomirov AN. Limit theorems for spectra of random matrices with martingale structure. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2006;51(1):42-64.We study classical ensembles of real symmetric random matrices introduced by Eugene Wigner. We discuss Stein's method for the asymptotic approximation of expectations of functions of the normalized eigenvalue counting measure of high dimensional matrices. The method is based on a differential equation for the density of the semicircle law