{"type":"journal_article","author":[{"last_name":"Bourgade","full_name":"Bourgade, Paul","first_name":"Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"László Erdös","first_name":"László","last_name":"Erdös"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng-Tzer"}],"doi":"10.1063/1.4751478","issue":"9","day":"28","publist_id":"4112","date_updated":"2021-01-12T06:59:38Z","intvolume":"        53","publisher":"American Institute of Physics","citation":{"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>.","short":"P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (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>","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.","ista":"Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9).","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>","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>."},"status":"public","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."}],"month":"09","_id":"2778","publication":"Journal of Mathematical Physics","year":"2012","date_published":"2012-09-28T00:00:00Z","volume":53,"publication_status":"published","quality_controlled":0,"date_created":"2018-12-11T11:59:33Z","title":"Bulk universality of general β-ensembles with non-convex potential","extern":1}