Evolution of the interfaces in a two dimensional Potts model

Details Evolution of the interfaces in a two dimensional Potts model Evolution of the interfaces in a two dimensional Potts model

2006-08-06

arxiv.org/abs/math/0608142v2

Mathematics

Probability

31 pages

Scientific paper

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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