Propagation of Chaos for 2D Log Gas on the Whole Space

TL;DR

This paper establishes the propagation of chaos for 2D Log gas systems on the whole space using a novel adaptation of the modulated free energy method, providing quantitative entropy-based results.

Contribution

It extends the propagation of chaos results to the 2D Log gas on the whole space by adapting existing methods and deriving key growth estimates.

Findings

Quantitative propagation of chaos in relative entropy for 2D Log gas.

Extension of the modulated free energy method to whole space setting.

Logarithmic growth estimates for the mean-field PNP equation.

Abstract

We derive the quantitative propagation of chaos in the sense of relative entropy for the first time for the 2D Log gas or the weakly interacting particle systems with 2D Coulomb interactions on the whole space. We resolve this problem by adapting the modulated free energy method in [BJW23] to the whole space setting and establishing the crucial logarithmic growth estimates for the mean-field Poisson-Nernst-Planck (PNP) equation of single component via the parabolic maximum principle.