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Large deviations for mean field models of probabilistic cellular automata
Author(s) -
Balister P.,
Bollobás B.,
Kozma R.
Publication year - 2006
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20126
Subject(s) - cellular automaton , mean field theory , statistical physics , probabilistic logic , stochastic cellular automaton , range (aeronautics) , field (mathematics) , mathematics , computer science , algorithm , statistics , physics , pure mathematics , quantum mechanics , composite material , materials science
Probabilistic cellular automata form a very large and general class of stochastic processes. These automata exhibit a wide range of complex behavior and are of interest in a number of fields of study, including mathematical physics, percolation theory, computer science, and neurobiology. Very little has been proved about these models, even in simple cases, so it is common to compare the models to mean field models. It is normally assumed that mean field models are essentially trivial. However, we show here that even the mean field models can exhibit surprising behavior. We prove some rigorous results on mean field models, including the existence of a surrogate for the “energy” in certain non‐reversible models. We also briefly discuss some differences that occur between the mean field and lattice models. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006