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

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

2008-04-14

arxiv.org/abs/0804.2116v1

Physics

Mathematical Physics

37 pages, 1 figure

Scientific paper

We consider the deformed Gaussian Ensemble $H_n=M_n+H^{(0)}_n$ 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 $H_n$.

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