Application to Probabilistic Cellular Automata

AbstractWe consider the problem of metastability for stochastic dynamics with exponentially small transition probabilities in the low temperature limit. We generalize previous model-independent results in several directions. First, we give an estimate of the mixing time of the dynamics in terms of the maximal stability level. Second, assuming the dynamics is reversible, we give an estimate of the associated spectral gap. Third, we give precise asymptotics for the expected transition time from any metastable state to the stable state using potential-theoretic techniques. We do this in a general... Mehr ...

Verfasser: Francesca R. Nardi
Gianmarco Bet
Vanessa Jacquier
Dokumenttyp: Artikel
Erscheinungsdatum: 2020
Schlagwörter: Netherlands / Netherlands Organisation for Scientific Research (NWO) / Knowmad Institut / Mathematical Physics / Statistical and Nonlinear Physics
Sprache: Englisch
Permalink: https://search.fid-benelux.de/Record/base-26811655
Datenquelle: BASE; Originalkatalog
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Link(s) : https://www.openaccessrepository.it/record/80753

AbstractWe consider the problem of metastability for stochastic dynamics with exponentially small transition probabilities in the low temperature limit. We generalize previous model-independent results in several directions. First, we give an estimate of the mixing time of the dynamics in terms of the maximal stability level. Second, assuming the dynamics is reversible, we give an estimate of the associated spectral gap. Third, we give precise asymptotics for the expected transition time from any metastable state to the stable state using potential-theoretic techniques. We do this in a general reversible setting where two or more metastable states are allowed and some of them may even be degenerate. This generalizes previous results that hold for a series of only two metastable states. We then focus on a specific Probabilistic Cellular Automata (PCA) with configuration space $$