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Bibliographic Details
Main Authors: Padilla-Garza, David, Peilen, Luke, Thoma, Eric
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.02625
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author Padilla-Garza, David
Peilen, Luke
Thoma, Eric
author_facet Padilla-Garza, David
Peilen, Luke
Thoma, Eric
contents We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse temperature $β$ satisfies $N^{-1} \ll β\ll N^{-\frac{1}{2}}$, where $N$ is the number of particles. This expands the temperature regime for which convergence to a Poisson point process has been proved.
format Preprint
id arxiv_https___arxiv_org_abs_2405_02625
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Emergence of a Poisson process in weakly interacting particle systems
Padilla-Garza, David
Peilen, Luke
Thoma, Eric
Probability
We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse temperature $β$ satisfies $N^{-1} \ll β\ll N^{-\frac{1}{2}}$, where $N$ is the number of particles. This expands the temperature regime for which convergence to a Poisson point process has been proved.
title Emergence of a Poisson process in weakly interacting particle systems
topic Probability
url https://arxiv.org/abs/2405.02625