Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata
(2012) Journal of Statistical Physics — Vol. 147, n° 3, p. 634-652 (2012)
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- Abstract
- We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of Toom. They are defined as stochastic perturbations of cellular automata belonging to the category of monotonic binary tessellations and possessing a property of erosion. We prove, for a set of initial conditions, exponential convergence of the induced processes toward an extremal invariant measure with a highly predominant spin value. We also show that this invariant measure presents exponential decay of correlations in space and in time and is therefore strongly mixing.
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de Maere d’Aertrycke, A., & Ponselet, L. (2012). Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata. Journal of Statistical Physics, 147(3), 634-652. https://doi.org/10.1007/s10955-012-0487-9 (Original work published 2012)