Markovianity of the invariant distribution of probabilistic cellular\n automata on the line

2014/01/21 by Jérôme Casse, Casse, Jérôme, Jean‐François Marckert +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #37A25 #37B15 #60J22 #60K35 #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1401.5365

openalex publication_date 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the problem of finding the conditions under which synchronous\nprobabilistic cellular automata indexed by the line \ℤ, or the\nperiodic line cyln, depending on 2 neighbours, admit as invariant\ndistribution the law of a space-indexed Markov chain. Our advances concerns PCA\ndefined on a finite alphabet, where most of existing results concern size 2\nalphabet. A part of the paper is also devoted to the comparison of different\nstructures (\ℤ, cyln, and also some structures constituted with\ntwo consecutive lines of the space time diagram) with respect to the property\nto possess a Markovian invariant distribution.\n

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