On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble

Abstract

We consider the deformed Gaussian Ensemble Hn = Hn⁽⁰⁾ +Mn in which Hn⁽⁰⁾ is a hermitian matrix (possibly random) and Mn is the Gaussian Unitary Ensemble (GUE) random matrix (independent of Hn⁽⁰⁾ ). Assuming that the Normalized Counting Measure of Hn⁽⁰⁾converges weakly (in probability) to a nonrandom measure N⁽⁰⁾ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.