{"_id":"2778","abstract":[{"lang":"eng","text":"We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β &gt; 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a &quot;convexified measure&quot; so that the local statistics are preserved under this convexification."}],"status":"public","extern":1,"type":"journal_article","publication":"Journal of Mathematical Physics","author":[{"first_name":"Paul","full_name":"Bourgade, Paul","last_name":"Bourgade"},{"full_name":"László Erdös","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Horng","full_name":"Yau, Horng-Tzer","last_name":"Yau"}],"publisher":"American Institute of Physics","day":"28","issue":"9","title":"Bulk universality of general β-ensembles with non-convex potential","volume":53,"year":"2012","intvolume":"        53","date_created":"2018-12-11T11:59:33Z","date_updated":"2021-01-12T06:59:38Z","citation":{"short":"P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (2012).","ista":"Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9).","mla":"Bourgade, Paul, et al. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” <i>Journal of Mathematical Physics</i>, vol. 53, no. 9, American Institute of Physics, 2012, doi:<a href=\"https://doi.org/10.1063/1.4751478\">10.1063/1.4751478</a>.","ieee":"P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” <i>Journal of Mathematical Physics</i>, vol. 53, no. 9. American Institute of Physics, 2012.","ama":"Bourgade P, Erdös L, Yau H. Bulk universality of general β-ensembles with non-convex potential. <i>Journal of Mathematical Physics</i>. 2012;53(9). doi:<a href=\"https://doi.org/10.1063/1.4751478\">10.1063/1.4751478</a>","chicago":"Bourgade, Paul, László Erdös, and Horng Yau. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 2012. <a href=\"https://doi.org/10.1063/1.4751478\">https://doi.org/10.1063/1.4751478</a>.","apa":"Bourgade, P., Erdös, L., &#38; Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.4751478\">https://doi.org/10.1063/1.4751478</a>"},"doi":"10.1063/1.4751478","month":"09","publication_status":"published","date_published":"2012-09-28T00:00:00Z","quality_controlled":0,"publist_id":"4112"}