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

Abstract

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.

76 pages

References in corpus (2)

• Local semicircle law and complete delocalization for Wigner random matrices
• Random matrices: Universality of local eigenvalue statistics

Cited by in corpus (4)

• Random matrices: Universality of local eigenvalue statistics up to the edge
• Random matrices: Universality of local eigenvalue statistics
• Random matrices: The Four Moment Theorem for Wigner ensembles
• The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices