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

Abstract

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 $H_n$.

25 pages, 2 figures

References in corpus (4)

• Random matrices: Universality of local eigenvalue statistics up to the edge
• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Bulk Universality and Related Properties of Hermitian Matrix Models
• Universality of Wigner Random Matrices

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