Evolution of the interfaces in a two dimensional Potts model

2006/08/06 by Glauco Valle, Valle, Glauco
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0608142

openalex publication_date 2006/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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