On universality of local edge regime for the deformed Gaussian Unitary Ensemble

Details On universality of local edge regime for the deformed Gaussian Unitary Ensemble On universality of local edge regime for the deformed Gaussian Unitary Ensemble

2011-01-10

arxiv.org/abs/1101.1813v1

Physics

Mathematical Physics

25 pages, 2 figures

Scientific paper

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 random matrix (GUE) independent of $H_n^{(0)}$. Assuming that the Normalized Counting Measure of $H_n^{(0)}$ converges weakly (in probability if random) to a non-random measure $N^{(0)}$ with a bounded support and assuming some conditions on the convergence rate, we prove universality of the local eigenvalue statistics near the edge of the limiting spectrum of $H_n$.

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