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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata

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Coletti, Cristian F. [1] ; Tisseur, Pierre [1]
Total Authors: 2
[1] Univ Fed ABC, Ctr Matemat Cognicao & Computacao, Santo Andre, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Journal of Statistical Physics; v. 140, n. 1, p. 103-121, JUL 2010.
Web of Science Citations: 3

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 explicitly all the constants involved. (AU)