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