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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 12 open journal systems 


Evolution of the interfaces in a two dimensional Potts model

Glauco Valle, UFRJ


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.


Full text: PDF

Pages: 354-386

Published on: April 5, 2007
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Electronic Journal of Probability. ISSN: 1083-6489