论文标题
本地法律和$β$增密的介观CLT
Local Laws and a Mesoscopic CLT for $β$-ensembles
论文作者
论文摘要
我们研究日志气体的统计力学，即$β$汇总的一般潜力和反向温度。通过引导程序，我们证明了下一个阶级能量的局部定律，该定律有效至显微镜长度尺度。据我们所知，这是第一次为log-Gas控制了这种局部数量。同时，我们对线性统计的波动进行了控制，这些波动在所有介质中都是有效的。使用这些局部定律，我们能够首次在任意介质上展示CLT，从而改善了仅对于功率中尺度的Bekerman-Lodhia的先前结果。
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 these local laws, we are able to exhibit for the first time a CLT at arbitrary mesoscales, improving upon a previous result of Bekerman-Lodhia that was true only for power mesoscales.
