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

2023/09/02 by Padilla-Garza, David
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.00961

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.

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