Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156222 | Stochastic Processes and their Applications | 2015 | 26 Pages |
Abstract
We revisit the problem of finding the conditions under which synchronous probabilistic cellular automata indexed by the line ZZ, or the periodic line Z/nZZ/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.A part of the paper is also devoted to the comparison of different structures (ZZ, Z/nZZ/nZ, and also some structures constituted with two consecutive lines of the space–time diagram) with respect to the property to possess a Markovian invariant distribution.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jérôme Casse, Jean-François Marckert,