Ergodicity of the hard-core PCA with a random walk method
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908416966918144 |
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| author | Casse, Jérôme Marcovici, Irène Poutrel, Maxence |
| author_facet | Casse, Jérôme Marcovici, Irène Poutrel, Maxence |
| contents | The hard-core probabilistic cellular automaton has attracted a renewed interest in the last few years, thanks to its connection with the study of a combinatorial game on percolation configurations. We provide an alternative proof for the ergodicity of this PCA for a neighbourhood of size $2$ and $3$, using the notion of decorrelated islands introduced by Casse in 2023, together with some new ideas. This shortens the previous proofs and provides a more intuitive and unified approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity of the hard-core PCA with a random walk method Casse, Jérôme Marcovici, Irène Poutrel, Maxence Probability 60K35, 60J05, 37B15, 05C57 The hard-core probabilistic cellular automaton has attracted a renewed interest in the last few years, thanks to its connection with the study of a combinatorial game on percolation configurations. We provide an alternative proof for the ergodicity of this PCA for a neighbourhood of size $2$ and $3$, using the notion of decorrelated islands introduced by Casse in 2023, together with some new ideas. This shortens the previous proofs and provides a more intuitive and unified approach. |
| title | Ergodicity of the hard-core PCA with a random walk method |
| topic | Probability 60K35, 60J05, 37B15, 05C57 |
| url | https://arxiv.org/abs/2506.18632 |