Front progression in the East model |
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Authors: | Oriane Blondel |
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Institution: | Univ. Paris Diderot, Sorbonne Paris Cité, LPMA, UMR 7599, Bâtiment Sophie Germain, 5 rue Thomas Mann, 75205 Paris CEDEX 13, France |
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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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Keywords: | Shape theorem Invariant measure Out of equilibrium dynamics KCSM Coupling |
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