Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155517 | Stochastic Processes and their Applications | 2013 | 36 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Oriane Blondel,