Erdos, LaszloRamirez, JoseSchlein, BenjaminYau, Horng-Tzer2017-04-172010Erdős, Laszlo, Jose Ramirez, Benjamin Schlein, and Horng-Tzer Yau. 2010. “Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation.” Electronic Journal of Probability 15 (0): 526–604. doi:10.1214/ejp.v15-768.1083-6489http://nrs.harvard.edu/urn-3:HUL.InstRepos:32189256We 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+βN−3/4+β for some positive β>0β>0. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.en-USWigner random matrixDyson sine kernelJournal Article2017-04-1710.1214/EJP.v15-768