Gaussian concentration bounds for probabilistic cellular automata
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915376604905472 |
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| author | Chazottes, Jean-René Redig, Frank Ugalde, Edgardo |
| author_facet | Chazottes, Jean-René Redig, Frank Ugalde, Edgardo |
| contents | We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish the conservation of GCB and, in the high-noise regime, demonstrate that GCB holds for the unique stationary measure. Additionally, we prove the equivalence of GCB for the space-time measure and its spatial marginals in the case of contractive probabilistic cellular automata. Furthermore, we explore the relationship between (non)-uniqueness and GCB in the context of space-time Gibbs measures for PCA and illustrate these results with examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian concentration bounds for probabilistic cellular automata Chazottes, Jean-René Redig, Frank Ugalde, Edgardo Probability 60K36, 60J05, 37B15, 37A50 We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish the conservation of GCB and, in the high-noise regime, demonstrate that GCB holds for the unique stationary measure. Additionally, we prove the equivalence of GCB for the space-time measure and its spatial marginals in the case of contractive probabilistic cellular automata. Furthermore, we explore the relationship between (non)-uniqueness and GCB in the context of space-time Gibbs measures for PCA and illustrate these results with examples. |
| title | Gaussian concentration bounds for probabilistic cellular automata |
| topic | Probability 60K36, 60J05, 37B15, 37A50 |
| url | https://arxiv.org/abs/2507.05431 |