Ergodicity Criterion for One-Sided, One-Dimensional IPS with a Long-Lived State
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913985534623744 |
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| author | Gluchowski, Maciej Menz, Georg |
| author_facet | Gluchowski, Maciej Menz, Georg |
| contents | We study one-dimensional, one-sided, nearest-neighbor Interacting Particle Systems (IPS) with positive rates and identify a criterion for ergodicity based on the presence of a long lived state a site can occupy. The criterion is that the IPS admits a state with a ratio of rates of exiting to entering below~$\sqrt{2}$. The main idea is that under the canonical coupling, it is possible to identify large blocks in spacetime where two coupled trajectories must agree to share the special state, which inhibits the spread of disagreement. The result covers much of the parameter region left open by earlier work on the Positive Rates Conjecture (PRC) for simple IPS, narrowing the unresolved IPS to noisy versions of the East model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity Criterion for One-Sided, One-Dimensional IPS with a Long-Lived State Gluchowski, Maciej Menz, Georg Probability 60K35, 82C22 We study one-dimensional, one-sided, nearest-neighbor Interacting Particle Systems (IPS) with positive rates and identify a criterion for ergodicity based on the presence of a long lived state a site can occupy. The criterion is that the IPS admits a state with a ratio of rates of exiting to entering below~$\sqrt{2}$. The main idea is that under the canonical coupling, it is possible to identify large blocks in spacetime where two coupled trajectories must agree to share the special state, which inhibits the spread of disagreement. The result covers much of the parameter region left open by earlier work on the Positive Rates Conjecture (PRC) for simple IPS, narrowing the unresolved IPS to noisy versions of the East model. |
| title | Ergodicity Criterion for One-Sided, One-Dimensional IPS with a Long-Lived State |
| topic | Probability 60K35, 82C22 |
| url | https://arxiv.org/abs/2508.08459 |