@article{2764,
abstract = {Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any β≥1, we prove that the relaxation time to local equilibrium for the Dyson Brownian motion is bounded above by N -ζ for some ζ> 0. The proof is based on an estimate of the entropy flow of the Dyson Brownian motion w. r. t. a "pseudo equilibrium measure". As an application of this estimate, we prove that the eigenvalue spacing statistics in the bulk of the spectrum for N×N symmetric Wigner ensemble is the same as that of the Gaussian Orthogonal Ensemble (GOE) in the limit N→∞. The assumptions on the probability distribution of the matrix elements of the Wigner ensemble are a subexponential decay and some minor restriction on the support.},
author = {László Erdös and Schlein, Benjamin and Yau, Horng-Tzer},
journal = {Inventiones Mathematicae},
number = {1},
pages = {75 -- 119},
publisher = {Springer},
title = {{Universality of random matrices and local relaxation flow}},
doi = {10.1007/s00222-010-0302-7},
volume = {185},
year = {2011},
}