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- W4299495959 abstract "A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. We investigate the ergodicity of this Markov chain. A classical cellular automaton is a particular case of PCA. For a 1-dimensional cellular automaton, we prove that ergodicity is equivalent to nilpotency, and is therefore undecidable. We then propose an efficient perfect sampling algorithm for the invariant measure of an ergodic PCA. Our algorithm does not assume any monotonicity property of the local rule. It is based on a bounding process which is shown to be also a PCA. Last, we focus on the PCA Majority, whose asymptotic behavior is unknown, and perform numerical experiments using the perfect sampling procedure." @default.
- W4299495959 created "2022-10-02" @default.
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- W4299495959 date "2010-10-15" @default.
- W4299495959 modified "2023-09-27" @default.
- W4299495959 title "Probabilistic cellular automata, invariant measures, and perfect sampling" @default.
- W4299495959 doi "https://doi.org/10.48550/arxiv.1010.3133" @default.
- W4299495959 hasPublicationYear "2010" @default.
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