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Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule

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Abstract

In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an exponential random variable and that the rate of the exponential random variable is an exponential function of the inverse temperature β times a prefactor that does not scale with β. Our approach combines geometric and potential theoretic arguments.

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Authors and Affiliations

  1. EURANDOM, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    F. R. Nardi

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    F. R. Nardi

  3. Department of Medical Statistics and Bioinformatics, Leiden University Medical Centre, P.O. Box 9600, 2300 RC, Leiden, The Netherlands

    C. Spitoni

Authors
  1. F. R. Nardi
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  2. C. Spitoni
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Correspondence to C. Spitoni.

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Nardi, F.R., Spitoni, C. Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule. J Stat Phys 146, 701–718 (2012). https://doi.org/10.1007/s10955-011-0413-6

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  • DOI: https://doi.org/10.1007/s10955-011-0413-6

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