Time-Periodic Behaviour in One- and Two-Dimensional Interacting Particle Systems

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2025年9月17日

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Benedikt Jahnel,
Jonas Köppl

摘要

We provide a class of examples of interacting particle systems on $\mathbb {Z}^d$ $Z^{d}$ , for $d\in \{1,2\}$ $d \in {1, 2}$ , 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.