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arXiv · 2402.12300

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

Jonas Köppl·Benedikt Jahnel
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Abstract

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.

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Jonas Köppl, Benedikt Jahnel. 2024-02-19. Time-periodic behaviour in one- and two-dimensional interacting particle systems. https://doi.org/10.1007/s00023-025-01624-5

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