Bulk Universality for Wigner Matrices

We consider N x N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density v(x) = e(-U(x)). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U is an element of C(6)(R) with at most polynomially growing derivatives and v(x) <= C e(-C vertical bar x vertical bar) 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. (C) 2010 Wiley Periodicals, Inc.