--- res: bibo_abstract: - We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Paul foaf_name: Bourgade, Paul foaf_surname: Bourgade - foaf_Person: foaf_givenName: László foaf_name: Erdös, László foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Horngtzer foaf_name: Yau, Horngtzer foaf_surname: Yau - foaf_Person: foaf_givenName: Jun foaf_name: Yin, Jun foaf_surname: Yin bibo_doi: 10.1002/cpa.21624 bibo_issue: '10' bibo_volume: 69 dct_date: 2016^xs_gYear dct_language: eng dct_publisher: Wiley-Blackwell@ dct_title: Fixed energy universality for generalized wigner matrices@ ...