On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble - Shcherbina, T. (Журнал математичної фізики, аналізу, геометрії, 2009)
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 measureN^(0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of H_n. Mathematics Subject Classification: 15A52, 15A57.