--- res: bibo_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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: László foaf_name: László Erdös foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Benjamin foaf_name: Schlein, Benjamin foaf_surname: Schlein - foaf_Person: foaf_givenName: Horng foaf_name: Yau, Horng-Tzer foaf_surname: Yau bibo_doi: 10.1007/s00222-010-0302-7 bibo_issue: '1' bibo_volume: 185 dct_date: 2011^xs_gYear dct_publisher: Springer@ dct_title: Universality of random matrices and local relaxation flow@ ...