Large deviations for the two-dimensional two-component plasma

TL;DR

This paper establishes a large deviations principle for the 2D two-component plasma, providing a variational formula for free energy and showing convergence of empirical measures to uniform distribution, with applications to complex Gaussian chaos.

Contribution

It introduces a large deviations framework for the 2D two-component plasma and connects it to free energy and empirical measure convergence, extending understanding of plasma behavior.

Findings

Large deviations principle derived for the plasma.

Variational representation for free energy obtained.

Empirical measures converge to uniform distribution.

Abstract

We derive a large deviations principle for the two-dimensional two-component plasma in a box. As a consequence, we obtain a variational representation for the free energy, and also show that the macroscopic empirical measure of either positive or negative charges converges to the uniform measure. An appendix, written by Wei Wu, discusses applications to the supercritical complex Gaussian multiplicative chaos.