标题： 平面库仑气体的孔概率和测度的扫除 显示英文标题

标题： Hole probabilities and balayage of measures for planar Coulomb gases

摘要： 我们研究具有通用势和任意温度的二维库仑气体的空洞概率。 空洞区域$U$被假定满足$\partial U\subset S$，其中$S$是平衡测度的支撑集$\mu$。 令$n$为点的数量。 如$n \to \infty$所示，我们证明没有点位于$U$的概率类似于$\exp(-Cn^{2}+o(n^{2}))$。 我们根据$\mu$和平衡测度$\nu = \mathrm{Bal}(\mu|_{U},\partial U)$确定$C$。 如果$U$无界，则$C$还涉及$\Omega$在点$\infty$处的格林函数，其中$\Omega$是$U$的无界分支。 我们还提供了一些例子，其中$\nu$和$C$可以有显式表达式：我们考虑了几种点过程，如椭圆Ginibre点过程、Mittag-Leffler点过程和球面点过程，以及各种空洞区域，如圆弧、椭圆、矩形和椭圆的补集。 这项工作在多个方向上推广了Adhikari和Reddy之前的成果。 显示英文摘要

摘要： We study hole probabilities of two-dimensional Coulomb gases with a general potential and arbitrary temperature. The hole region $U$ is assumed to satisfy $\partial U\subset S$, where $S$ is the support of the equilibrium measure $\mu$. Let $n$ be the number of points. As $n \to \infty$, we prove that the probability that no points lie in $U$ behaves like $\exp(-Cn^{2}+o(n^{2}))$. We determine $C$ in terms of $\mu$ and the balayage measure $\nu = \mathrm{Bal}(\mu|_{U},\partial U)$. If $U$ is unbounded, then $C$ also involves the Green function of $\Omega$ with pole at $\infty$, where $\Omega$ is the unbounded component of $U$. We also provide several examples where $\nu$ and $C$ admit explicit expressions: we consider several point processes, such as the elliptic Ginibre, Mittag-Leffler, and spherical point processes, and various hole regions, such as circular sectors, ellipses, rectangles, and the complement of an ellipse. This work generalizes previous results of Adhikari and Reddy in several directions.