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Front progression for the East model | | Oriane Blondel
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18 Dec 2012 | | 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. | | Source: | arXiv, 1212.4435 | | Services: | Forum | Review | PDF | Favorites | |
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