Ergodicity of the hard-core PCA with a random walk method

Jérôme Casse; Irène Marcovici; Maxence Poutrel

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arXiv · 2506.18632

Ergodicity of the hard-core PCA with a random walk method

Jérôme Casse·Irène Marcovici·Maxence Poutrel

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Abstract

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.

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Jérôme Casse, Irène Marcovici, Maxence Poutrel. 2025-06-23. Ergodicity of the hard-core PCA with a random walk method. https://arxiv.org/abs/2506.18632

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