β系综的局域定律和介观CLT

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-10-08 DOI:10.1002/cpa.22175

Luke Peilen

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引用次数: 0

摘要

我们研究了对数气体或β系综在一般势和反温度下的统计力学。通过bootstrap过程，我们证明了下一阶能量的局部定律在微观长度尺度上是有效的。据我们所知，这是第一次对原木气进行这种局部量的控制。同时，我们使用Johansson方法和输运方法展示了对线性统计波动的控制，该控制在所有细尺度上都是有效的。使用这些局部定律，我们首次能够在任意中尺度上展示CLT，改进了以前仅适用于功率中尺度的结果。

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Local laws and a mesoscopic CLT for β-ensembles

We study the statistical mechanics of the log-gas, or β-ensemble, for general potential and inverse temperature. By means of a bootstrap procedure, we prove local laws on the next order energy that are valid down to microscopic length scales. To our knowledge, this is the first time that this kind of a local quantity has been controlled for the log-gas. Simultaneously, we exhibit a control on fluctuations of linear statistics that is valid at all mesoscales using Johansson's method and a transport approach. Using these local laws, we are able to exhibit for the first time a CLT at arbitrary mesoscales, improving upon previous results that were true only for power mesoscales.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.