On the long-time behaviour of reversible interacting particle systems in one and two dimensions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915329078198272 |
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| author | Jahnel, Benedikt Köppl, Jonas |
| author_facet | Jahnel, Benedikt Köppl, Jonas |
| contents | By refining Holley's free energy technique, we show that, under quite general assumptions on the dynamics, the attractor of a (possibly non-translation-invariant) interacting particle system in one or two spatial dimensions is contained in the set of Gibbs measures if the dynamics admits a reversible Gibbs measure. In particular, this implies that there can be no reversible interacting particle system that exhibits time-periodic behaviour and that every reversible interacting particle system is ergodic if and only if the reversible Gibbs measure is unique. In the special case of non-attractive stochastic Ising models this answers a question due to Liggett. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_10640 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the long-time behaviour of reversible interacting particle systems in one and two dimensions Jahnel, Benedikt Köppl, Jonas Probability Mathematical Physics Primary 82C22, Secondary 60K35 By refining Holley's free energy technique, we show that, under quite general assumptions on the dynamics, the attractor of a (possibly non-translation-invariant) interacting particle system in one or two spatial dimensions is contained in the set of Gibbs measures if the dynamics admits a reversible Gibbs measure. In particular, this implies that there can be no reversible interacting particle system that exhibits time-periodic behaviour and that every reversible interacting particle system is ergodic if and only if the reversible Gibbs measure is unique. In the special case of non-attractive stochastic Ising models this answers a question due to Liggett. |
| title | On the long-time behaviour of reversible interacting particle systems in one and two dimensions |
| topic | Probability Mathematical Physics Primary 82C22, Secondary 60K35 |
| url | https://arxiv.org/abs/2303.10640 |