@article{2767, abstract = {Consider N × N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure ν ij with a subexponential decay. Let σ ij 2 be the variance for the probability measure ν ij with the normalization property that Σ iσ i,j 2 = 1 for all j. Under essentially the only condition that c ≤ N σ ij 2 ≤ c -1 for some constant c > 0, we prove that, in the limit N → ∞, 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. }, author = {László Erdös and Yau, Horng-Tzer and Yin, Jun}, journal = {Probability Theory and Related Fields}, number = {1-2}, pages = {341 -- 407}, publisher = {Springer}, title = {{Bulk universality for generalized Wigner matrices}}, doi = {10.1007/s00440-011-0390-3}, volume = {154}, year = {2012}, }