Front progression for the East model

Abstract : The East model is a one-dimensional, non-attractive interacting particle system with Glauber dynamics, in which a flip is prohibited at a site $x$ if the right neighbour $x+1$ is occupied. Starting from a configuration entirely occupied on the left half-line, we prove a law of large numbers for the position of the left-most zero (the front), as well as ergodicity of the process seen from the front. For want of attractiveness, the one-dimensional shape theorem is not derived by the usual coupling arguments, but instead by quantifying the local relaxation to the non-equilibrium invariant measure for the process seen from the front. This is the first proof of a shape theorem for a kinetically constrained spin model.
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Stochastic Processes and their Applications, Elsevier, 2013, Vol 123, Issue 9, p. 3430-3465
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Contributeur : Oriane Blondel <>
Soumis le : mercredi 19 décembre 2012 - 10:42:01
Dernière modification le : vendredi 28 avril 2017 - 01:02:46

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  • HAL Id : hal-00766855, version 1
  • ARXIV : 1212.4435

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Oriane Blondel. Front progression for the East model. Stochastic Processes and their Applications, Elsevier, 2013, Vol 123, Issue 9, p. 3430-3465. 〈hal-00766855〉

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