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

Abstract

We consider the deformed Gaussian Ensemble $H_n=M_n+H_n^{(0)}$ in which $H_n^{(0)}$ is a diagonal Hermitian matrix and $M_n$ is the Gaussian Unitary Ensemble (GUE) random matrix. Assuming that the Normalized Counting Measure of $H_n^{(0)}$ (both non-random and random) converges weakly to a measure $N^{(0)}$ with a bounded support we prove universality of the local eigenvalue statistics in the bulk of the limiting spectrum of $H_n$.

37 pages, 1 figure