Erdos, LaszloPéché, SandrineRamírez, José A.Schlein, BenjaminYau, Horng-Tzer2017-05-182010Erdős, László, Sandrine Péché, José A. Ramírez, Benjamin Schlein, and Horng-Tzer Yau. 2010. “Bulk Universality for Wigner Matrices.” Communications on Pure and Applied Mathematics. doi:10.1002/cpa.20317.0010-3640http://nrs.harvard.edu/urn-3:HUL.InstRepos:32706723We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e−U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U ∈ C6( \input amssym $\Bbb R$) with at most polynomially growing derivatives and ν(x) ≥ Ce−C|x| for x large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales. © 2010 Wiley Periodicals, Inc.en-USWigner random matrixDyson sine kernelJournal Article2017-05-1810.1002/cpa.20317