TY - JOUR
AB - We 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.
AU - Bourgade, Paul
AU - László Erdös
AU - Yau, Horng-Tzer
ID - 2778
IS - 9
JF - Journal of Mathematical Physics
TI - Bulk universality of general β-ensembles with non-convex potential
VL - 53
ER -