# 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.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2013, Vol 123, Issue 9, p. 3430-3465
Domaine :

https://hal.archives-ouvertes.fr/hal-00766855
Contributeur : Oriane Blondel <>
Soumis le : mercredi 19 décembre 2012 - 10:42:01
Dernière modification le : jeudi 11 janvier 2018 - 06:12:29

### Identifiants

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

### Citation

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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