Bulk universality of general β-ensembles with non-convex potential

Paul Bourgade; László Erdos; Horng Tzer Yau

doi:10.1063/1.4751478

Bulk universality of general β-ensembles with non-convex potential

Paul Bourgade, László Erdos, Horng Tzer Yau

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	095221
Journal	Journal of Mathematical Physics
Volume	53
Issue number	9
DOIs	https://doi.org/10.1063/1.4751478
State	Published - Sep 28 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4751478

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Bulk universality of general β-ensembles with non-convex potential

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