TY - JOUR
AB - We consider N ×N Hermitian Wigner random matrices H where the probabilitydensity 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 ∈ C 6(R{double-struck}) with at most polynomially growing derivatives and v(x)≤C e-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.
AU - László Erdös
AU - Ramírez, José A
AU - Yau, Horng-Tzer
AU - Péché, Sandrine
AU - Schlein, Benjamin
ID - 2762
IS - 7
JF - Communications on Pure and Applied Mathematics
TI - Bulk universality for Wigner matrices
VL - 63
ER -