Bulk universality of general β-ensembles with non-convex potential
Bulk universality of general β-ensembles with non-convex potential
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DOI：
10.1063/1.4751478
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发表时间：
2012-01
影响因子：
1.3
通讯作者：
P. Bourgade;L. Erdős;H. Yau
中科院分区：
文献类型：
--
作者：
P. Bourgade;L. Erdős;H. Yau
证明了具有非凸正则解析势的β系综的体普适性。这消除了在早期的工作中出现的凸性假设[P. Bourgeon，L。鄂尔多斯和H.- T. Yau，Universality of general β-ensembles，preprint arXiv：0907.5605（2011）].凸性条件使我们能够使用对数Sobolev不等式来估计小概率事件。新的思想是引入一个“凸化测度”，使得局部统计量在这种凸化下保持不变。
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. Erdos, 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.