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

We consider the deformed Gaussian Ensemble H(n) = H(n)((0)) + M(n) in which H(n)((0)) is a hermitian matrix (possibly random) and M(n) is the Gaussian Unitary Ensemble (GUE) random matrix (independent of H(n)((0))). Assuming that the Normalized Counting Measure of H(n)((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 H(n).