Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation

Laszlo Erdos, Jose A. Ramirez, Benjamin Schlein, Horng-Tzer Yau

Published 2009-05-13, updated 2010-04-01Version 2

We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance $N^{-3/4+\beta}$ for some positive $\beta>0$. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.