Bourgade, PaulErdos, LaszloYau, Horng-Tzer2023-01-202012-09Bourgade, Paul, László Erdős, and Horng-Tzer Yau. 2012. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics 53 (9) (September): 095221. doi:10.1063/1.4751478. http://dx.doi.org/10.1063/1.4751478.0022-24881089-7658https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37374050We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 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 “convexified measure” so that the local statistics are preserved under this convexification.en-USMathematical PhysicsStatistical and Nonlinear PhysicsJournal Article2023-01-2010.1063/1.4751478