论文标题
在中等温度方面，库仑气体的局部经验度量的大偏差原理
Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime
论文作者
论文摘要
本文涉及中等温度状态下的库仑气体。我们定义了局部经验领域并确定临界温度缩放。我们表明，如果温度的缩放是超临界的，则局部经验场通过基于熵的速率函数满足不发呆的。我们还表明，如果温度的缩放是亚临界的，则局部经验场可满足具有基于能量的速率功能的最不发达国家。在临界温度缩放方案中，我们得出了一个开拓性型结果，其中“速率函数”以熵和能量项的竞争为特征。这项工作的一个重要想法是利用库仑能量和熵满足的不同规模关系。
This paper deals with Coulomb gases at an intermediate temperature regime. We define a local empirical field and identify a critical temperature scaling. We show that if the scaling of the temperature is supercritical, the local empirical field satisfies an LDP with an entropy-based rate function. We also show that if the scaling of the temperature is subcritical, the local empirical field satisfies an LDP with an energy-based rate function. In the critical temperature scaling regime, we derive an LDP-type result in which the "rate function" features the competition of an entropy and energy terms. An important idea in this work is to exploit the different scaling relations satisfied by the Coulomb energy and the entropy.
