Publication: Bulk universality of general β-ensembles with non-convex potential
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Date
2012-09
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AIP Publishing
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Bourgade, 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.
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.
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Mathematical Physics, Statistical and Nonlinear Physics
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