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

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

2009-05-13

arxiv.org/abs/0905.2089v2

Physics

Mathematical Physics

76 pages

Scientific paper

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.

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