{"publication":"Advances in Theoretical and Mathematical Physics","abstract":[{"lang":"eng","text":"We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices."}],"citation":{"ista":"Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.","ama":"Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):739-800. doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">10.4310/ATMP.2017.v21.n3.a5</a>","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3. International Press, pp. 739–800, 2017.","apa":"Bourgade, P., Erdös, L., Yau, H., &#38; Yin, J. (2017). Universality for a class of random band matrices. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">https://doi.org/10.4310/ATMP.2017.v21.n3.a5</a>","mla":"Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3, International Press, 2017, pp. 739–800, doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">10.4310/ATMP.2017.v21.n3.a5</a>.","chicago":"Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2017. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">https://doi.org/10.4310/ATMP.2017.v21.n3.a5</a>."},"publication_identifier":{"issn":["10950761"]},"issue":"3","scopus_import":1,"oa":1,"oa_version":"Submitted Version","date_published":"2017-08-25T00:00:00Z","ec_funded":1,"title":"Universality for a class of random band matrices","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:46:43Z","date_updated":"2021-01-12T08:00:57Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02312"}],"author":[{"first_name":"Paul","full_name":"Bourgade, Paul","last_name":"Bourgade"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"},{"first_name":"Jun","last_name":"Yin","full_name":"Yin, Jun"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"International Press","publist_id":"7337","year":"2017","day":"25","month":"08","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"publication_status":"published","status":"public","volume":21,"intvolume":"        21","doi":"10.4310/ATMP.2017.v21.n3.a5","quality_controlled":"1","type":"journal_article","department":[{"_id":"LaEr"}],"page":"739 - 800","_id":"483"}