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

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  • Casse, Jérôme
  • Marckert, Jean-François

Abstract

We revisit the problem of finding the conditions under which synchronous probabilistic cellular automata indexed by the line Z, or the periodic line Z/nZ, depending on 2 neighbours, admit as invariant distribution the law of a space-indexed Markov chain. Our advances concern PCA defined on a finite alphabet, where most of existing results concern size 2 alphabet.

Suggested Citation

  • Casse, Jérôme & Marckert, Jean-François, 2015. "Markovianity of the invariant distribution of probabilistic cellular automata on the line," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3458-3483.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:9:p:3458-3483
    DOI: 10.1016/j.spa.2015.05.001
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    References listed on IDEAS

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    1. Bastien Chopard & Alexandre Dupuis & Alexandre Masselot & Pascal Luthi, 2002. "Cellular Automata And Lattice Boltzmann Techniques: An Approach To Model And Simulate Complex Systems," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 5(02n03), pages 103-246.
    2. Chassaing, Philippe & Mairesse, Jean, 2011. "A non-ergodic probabilistic cellular automaton with a unique invariant measure," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2474-2487, November.
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