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

Анотація

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 $H_n$.

Mathematics Subject Classification: 15A52, 15A57.