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 Electronic Journal of Probability > Vol. 15(2010) > Paper 18 open journal systems 


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

Laszlo Erdos, LMU-University of Munich
Jose A. Ramirez, Universidad de Costa Rica
Benjamin Schlein, University of Bonn
Horng-Tzer Yau, Harvard University


Abstract
We consider N x 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.


Full text: PDF

Pages: 526-604

Published on: May 1, 2010
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Electronic Journal of Probability. ISSN: 1083-6489