Asymptotes of macroscopic observables in Gibbs measures of general interacting particle systems

TL;DR

This paper investigates the convergence behavior of Gibbs measures in interacting particle systems, providing concentration bounds and fluctuation estimates using a regularization technique based on parabolic flows.

Contribution

It introduces a novel regularization method for general interaction kernels to analyze asymptotic properties of Gibbs measures in particle systems.

Findings

Established concentration inequalities for Gibbs measures.

Derived estimates on the Laplace transform of fluctuations.

Analyzed convergence to mean-field density across temperature regimes.

Abstract

This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the number of particles tends to infinity. Our main results are concentration bounds, and estimates on the Laplace transform of fluctuations. The main technique is a regularization procedure for general interaction kernels, based on an associated parabolic flow.