Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
We consider N × 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+β for some positive β > 0. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.
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526 - 603
526 - 603
Institute of Mathematical Statistics