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2007 Evolution of the interfaces in a two dimensional Potts model
Glauco Valle
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Electron. J. Probab. 12: 354-386 (2007). DOI: 10.1214/EJP.v12-346

Abstract

We investigate the evolution of the random interfaces in a two dimensional Potts model at zero temperature under Glauber dynamics for some particular initial conditions. We prove that under space-time diffusive scaling the shape of the interfaces converges in probability to the solution of a non-linear parabolic equation. This Law of Large Numbers is obtained from the Hydrodynamic limit of a coupling between an exclusion process and an inhomogeneous one dimensional zero range process with asymmetry at the origin.

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Glauco Valle. "Evolution of the interfaces in a two dimensional Potts model." Electron. J. Probab. 12 354 - 386, 2007. https://doi.org/10.1214/EJP.v12-346

Information

Accepted: 5 April 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60092
MathSciNet: MR2299921
Digital Object Identifier: 10.1214/EJP.v12-346

Subjects:
Primary: 60K35

Keywords: Exclusion processes , Hydrodynamic limit , interface dynamics

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