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Convergence Time of Probabilistic Cellular Automata on the Torus

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Book cover Probabilistic Cellular Automata

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 27))

Abstract

Many probabilistic cellular automata (PCA) exhibit a transition from an ergodic to a non-ergodic regime. Namely, if the free parameter is above a certain critical threshold, the process converges to a state that does not depend on the initial state (ergodicity), whereas if the free parameter is below the threshold, then the process converges to a state that depends on the initial state (non-ergodicity). If one considers the corresponding model on a finite space, such a transition is not observed (the process is always ergodic), nevertheless the convergence time is “small” when the corresponding process on infinite space is ergodic and “large” when the corresponding process on infinite space is non-ergodic. We analyse this correspondence for Percolation PCA, a class of probabilistic cellular automata which are closely related to oriented percolation.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, Germany

    Lorenzo Taggi

  2. TU Darmstadt, Darmstadt, Deutschland

    Lorenzo Taggi

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  1. Lorenzo Taggi
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Correspondence to Lorenzo Taggi .

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Editors and Affiliations

  1. Laboratoire de Mathématiques et Applications UMR 7348, Université de Poitiers, CNRS, Poitiers, France

    Pierre-Yves Louis

  2. University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Francesca R. Nardi

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Taggi, L. (2018). Convergence Time of Probabilistic Cellular Automata on the Torus. In: Louis, PY., Nardi, F. (eds) Probabilistic Cellular Automata. Emergence, Complexity and Computation, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-65558-1_13

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  • DOI: https://doi.org/10.1007/978-3-319-65558-1_13

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  • Online ISBN: 978-3-319-65558-1

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