{"publisher":"Wiley-Blackwell","_id":"1280","ec_funded":1,"page":"1815 - 1881","year":"2016","day":"01","type":"journal_article","scopus_import":1,"date_updated":"2021-01-12T06:49:35Z","oa_version":"Preprint","month":"10","intvolume":"        69","date_published":"2016-10-01T00:00:00Z","publist_id":"6036","date_created":"2018-12-11T11:51:07Z","doi":"10.1002/cpa.21624","publication":"Communications on Pure and Applied Mathematics","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"}],"status":"public","acknowledgement":"The work of P.B. was partially supported by National Sci-\r\nence Foundation Grant DMS-1208859.  The work of L.E. was partially supported\r\nby ERC Advanced Grant RANMAT 338804.  The work of H.-T. Y. was partially\r\nsupported by National Science Foundation Grant DMS-1307444 and a Simons In-\r\nvestigator award.  The work of J.Y. was partially supported by National Science\r\nFoundation Grant DMS-1207961.  The major part of this research was conducted\r\nwhen all authors were visiting IAS and were also supported by National Science\r\nFoundation Grant DMS-1128255.","volume":69,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1407.5606"}],"oa":1,"issue":"10","publication_status":"published","author":[{"last_name":"Bourgade","full_name":"Bourgade, Paul","first_name":"Paul"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Horngtzer","full_name":"Yau, Horngtzer","last_name":"Yau"},{"full_name":"Yin, Jun","last_name":"Yin","first_name":"Jun"}],"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","title":"Fixed energy universality for generalized wigner matrices","abstract":[{"text":"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.","lang":"eng"}],"citation":{"apa":"Bourgade, P., Erdös, L., Yau, H., &#38; Yin, J. (2016). Fixed energy universality for generalized wigner matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1002/cpa.21624\">https://doi.org/10.1002/cpa.21624</a>","ama":"Bourgade P, Erdös L, Yau H, Yin J. Fixed energy universality for generalized wigner matrices. <i>Communications on Pure and Applied Mathematics</i>. 2016;69(10):1815-1881. doi:<a href=\"https://doi.org/10.1002/cpa.21624\">10.1002/cpa.21624</a>","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied Mathematics 69 (2016) 1815–1881.","mla":"Bourgade, Paul, et al. “Fixed Energy Universality for Generalized Wigner Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 69, no. 10, Wiley-Blackwell, 2016, pp. 1815–81, doi:<a href=\"https://doi.org/10.1002/cpa.21624\">10.1002/cpa.21624</a>.","chicago":"Bourgade, Paul, László Erdös, Horngtzer Yau, and Jun Yin. “Fixed Energy Universality for Generalized Wigner Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell, 2016. <a href=\"https://doi.org/10.1002/cpa.21624\">https://doi.org/10.1002/cpa.21624</a>.","ista":"Bourgade P, Erdös L, Yau H, Yin J. 2016. Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. 69(10), 1815–1881.","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for generalized wigner matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016."}}