Bulk universality for generalized Wigner matrices

Consider N x N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure nu (ij) with a subexponential decay. Let be the variance for the probability measure nu (ij) with the normalization property that for all j. Under essentially the only condition that for some constant c > 0, we prove that, in the limit N -> a, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M (-1).