Time-periodic behaviour in one- and two-dimensional interacting particle systems

Fuente: arXiv
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Main Authors: Köppl, Jonas, Jahnel, Benedikt
Format: Preprint
Published: 2024
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author Köppl, Jonas
Jahnel, Benedikt
author_facet Köppl, Jonas
Jahnel, Benedikt
contents We provide a class of examples of interacting particle systems on $\mathbb{Z}^d$, for $d\in\{1,2\}$, that admit a unique translation-invariant stationary measure, which is not the long-time limit of all translation-invariant starting measures, due to the existence of time-periodic orbits in the associated measure-valued dynamics. This is the first such example and shows that even in low dimensions, not every limit point of the measure-valued dynamics needs to be a time-stationary measure.
format Preprint
id arxiv_https___arxiv_org_abs_2402_12300
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Time-periodic behaviour in one- and two-dimensional interacting particle systems
Köppl, Jonas
Jahnel, Benedikt
Probability
Mathematical Physics
Dynamical Systems
Primary 82C22, Secondary 60K35
We provide a class of examples of interacting particle systems on $\mathbb{Z}^d$, for $d\in\{1,2\}$, that admit a unique translation-invariant stationary measure, which is not the long-time limit of all translation-invariant starting measures, due to the existence of time-periodic orbits in the associated measure-valued dynamics. This is the first such example and shows that even in low dimensions, not every limit point of the measure-valued dynamics needs to be a time-stationary measure.
title Time-periodic behaviour in one- and two-dimensional interacting particle systems
topic Probability
Mathematical Physics
Dynamical Systems
Primary 82C22, Secondary 60K35
url https://arxiv.org/abs/2402.12300