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Refined universality for critical KCM: lower bounds

Part of: Special processes Markov processes Combinatorial probability Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  03 March 2022

Ivailo Hartarsky Open the ORCID record for Ivailo Hartarsky [Opens in a new window]  and
Laure Marêché
Ivailo Hartarsky
Affiliation:
CEREMADE, CNRS, UMR 7534, Université Paris-Dauphine, PSL University, Place du Maréchal de Lattre de Tassigny, 75016 Paris, France
Laure Marêché*
Affiliation:
Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, 67000 Strasbourg, France
*
*Corresponding author. Email: laure.mareche@math.unistra.fr
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Abstract

We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions tightly linked to the monotone cellular automata called bootstrap percolation. There are three classes of such models, the most studied being the critical one. In a recent series of works by Martinelli, Morris, Toninelli and the authors, it was shown that the KCM counterparts of critical bootstrap percolation models with the same properties split into two classes with different behaviour. Together with the companion paper by the first author, our work determines the logarithm of the infection time up to a constant factor for all critical KCM, which were previously known only up to logarithmic corrections. This improves all previous results except for the Duarte-KCM, for which we give a new proof of the best result known. We establish that on this level of precision critical KCM have to be classified into seven categories instead of the two in bootstrap percolation. In the present work, we establish lower bounds for critical KCM in a unified way, also recovering the universality result of Toninelli and the authors and the Duarte model result of Martinelli, Toninelli and the second author.

Keywords

Kinetically constrained modelsbootstrap percolationuniversalityclassificationGlauber dynamicsspectral gap

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82C22: Interacting particle systems 60J27: Continuous-time Markov processes on discrete state spaces 60C05: Combinatorial probability
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 31 , Issue 5 , September 2022 , pp. 879 - 906
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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