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.