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

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 $N^{-3/4+β}$ for some positive $β>0$. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.

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