Poisson Statistics for Coulomb Gases at Intermediate Temperature Regimes

TL;DR

This paper studies the microscopic behavior of Coulomb gases in two dimensions at intermediate temperatures, showing convergence to a Poisson point process under specific temperature conditions, and introduces a new method for analyzing correlation functions.

Contribution

It extends previous results by establishing Poisson convergence at intermediate temperature regimes and develops a novel quantitative approach for correlation functions.

Findings

Microscopic point process converges to a Poisson process under certain temperature limits.

Provides a new quantitative asymptotic description of correlation functions.

Extends understanding of Coulomb gas behavior at intermediate temperatures.

Abstract

We consider the microscopic statistics of a Coulomb gas in $\mathbb{R}^2$ at intermediate temperatures. In particular, we show that the microscopic point process associated to the Coulomb gas converges to a homogeneous Poisson point process at intermediate temperature regimes $\beta N \rightarrow \infty$ and $\beta \sqrt{N} \log N \rightarrow 0$, extending previous results. Our approach relies on a novel quantitative asymptotic description of correlation functions, which is of its own interest.