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

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