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Law of Large Numbers for Non-Local Functions on Probabilistic Cellular Automata

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Abstract

We prove a multi-dimensional version of the law of large numbers for invariant measures of a large class of probabilistic cellular automata, whose transition probabilities satisfy some inequalities, which are known to assure their ergodicity. In some non-ergodic cases analogous results have been obtained for local functions. We deal with a larger class of functions, which includes some non-local ones.

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  1. Department of Statistics, Federal University of Pernambuco, Recife, PE, 50740-540, Brazil

    André Toom

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  1. André Toom
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Correspondence to André Toom.

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Toom, A. Law of Large Numbers for Non-Local Functions on Probabilistic Cellular Automata. J Stat Phys 133, 883–897 (2008). https://doi.org/10.1007/s10955-008-9643-7

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  • DOI: https://doi.org/10.1007/s10955-008-9643-7

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