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

Paul Bourgade, László Erdos, Horng Tzer Yau

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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 languageEnglish (US)
Article number095221
JournalJournal of Mathematical Physics
Issue number9
StatePublished - Sep 28 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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