Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular AutomataReport as inadecuate




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1 CMCC - Centro de Matematica, Computação e Cognição

Abstract : We give new sufficient ergodicity conditions for two-state probabilistic cellular automata PCA of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in the one dimensional case, we study some properties of the unique invariant measure and show that it is shift-mixing. Also, the decay of correlation is studied in detail. In this sense, the extended concept of duality gives exponential decay of correlation and allows to compute explicitily all the constants involved.





Author: Cristian Coletti - Pierre Tisseur -

Source: https://hal.archives-ouvertes.fr/



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