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| HAL: hal-00407940, version 2 |
| arXiv: 0907.4841 |
| DOI: 10.1007/s10955-010-9985-9 |
| Detailed view |  Export this paper |
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| Journal of Statistical Physics 140, 1 (2010) 103-121 |
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| Available versions: | v1 (2009-07-28) | v2 (2009-12-12) |
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| Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata |
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| Cristian Coletti 1Pierre Tisseur 1 |
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| (2010-08-02) |
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| 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. |
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| 1: | Centro de Matematica, Computação e Cognição (CMCC) |
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UFABC |
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| Subject | : | Mathematics/Dynamical Systems Mathematics/Probability Mathematics/Mathematical Physics |
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| hal-00407940, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00407940 | |
| oai:hal.archives-ouvertes.fr:hal-00407940 | |
| From: Pierre Tisseur | |
| Submitted on: Saturday, 12 December 2009 02:26:08 | |
| Updated on: Sunday, 1 July 2012 04:23:05 | |
