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

2025/06/23 by Casse, Jérôme, Marcovici, Irène, Poutrel, Maxence
#05C57 #37B15 #60J05 #60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.18632

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.

Citations

• On a class of probabilistic cellular automata with size-3 neighbourhood and their applications in percolation games
• Percolation games, probabilistic cellular automata, and the hard-core\n model
• Probabilistic cellular automata, invariant measures, and perfect sampling

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