Time-periodic behaviour in one- and two-dimensional interacting particle systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908553146531840 |
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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 |
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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 |