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

P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (2012).

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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.
Publishing Year
Date Published
2012-09-28
Journal Title
Journal of Mathematical Physics
Volume
53
Issue
9
IST-REx-ID

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Bourgade P, Erdös L, Yau H. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.4751478
Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics, 53(9). https://doi.org/10.1063/1.4751478
Bourgade, Paul, László Erdös, and Horng Yau. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics 53, no. 9 (2012). https://doi.org/10.1063/1.4751478.
P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9, 2012.
Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9).
Bourgade, Paul, et al. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.4751478.

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