A simple bound on fluctuations in the 3D Coulomb gas

TL;DR

This paper provides a new proof that, at low temperatures, the fluctuations of linear statistics in the 3D Coulomb gas are bounded by a constant times N^{1-2/d}, highlighting stability in the system.

Contribution

The paper introduces a novel proof technique establishing bounds on fluctuations in the 3D Coulomb gas at low temperatures.

Findings

Linear statistics are bounded by C N^{1-2/d} at low temperature.

The proof offers a new approach to understanding Coulomb gas fluctuations.

Results contribute to the theoretical understanding of particle interactions in Coulomb systems.

Abstract

The Coulomb gas models an interacting system of $N$ negatively charged particles. We give a new proof that, at sufficiently low temperature, smooth linear statistics $\sum_j \varphi(x_j)$ are bounded by $C N^{1-2/d}$.