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Abstract

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = eU(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that UC6( \input amssym $\Bbb R$) with at most polynomially growing derivatives and ν(x) ≥ CeC|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.