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Front progression in the East model

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  • Blondel, Oriane

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.

Suggested Citation

  • Blondel, Oriane, 2013. "Front progression in the East model," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3430-3465.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3430-3465
    DOI: 10.1016/j.spa.2013.04.014
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    Cited by:

    1. Viktor Bezborodov & Luca Persio & Tyll Krueger, 2021. "A Shape Theorem for a One-Dimensional Growing Particle System with a Bounded Number of Occupants per Site," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2265-2284, December.

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