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

David Padilla-Garza

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arXiv · 2309.00961

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

David Padilla-Garza

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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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David Padilla-Garza. 2023-09-02. Asymptotes of macroscopic observables in Gibbs measures of general interacting particle systems. https://arxiv.org/abs/2309.00961

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