Motion by curvature and large deviations for an interface dynamics on ${\mathbb{Z}}^2$

Abstract

We study large deviations for a Markov process on curves in ${\mathbb{Z}}^2$ mimicking the motion of an interface. Our dynamics can be tuned with a parameter $\beta$, which plays the role of an inverse temperature, and coincides at $\beta$ = $\infty$ with the zero-temperature Ising model with Glauber dynamics, where curves correspond to the boundaries of droplets of one phase immersed in a sea of the other one. We prove that contours typically follow a motion by curvature with an influence of the parameter $\beta$, and establish large deviations bounds at all large enough $\beta$ < $\infty$. The diffusion coefficient and mobility of the model are identified and correspond to those predicted in the literature.

arXiv commentAccepted version. The presentation has been greatly reworked and explanations added throughout the paper

References in corpus (11)

• Large deviations for the boundary driven symmetric simple exclusion process
• Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions
• Dynamical large deviations for the boundary driven weakly asymmetric exclusion process
• Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound
• Free boundary problems in PDEs and particle systems
• Motion by mean curvature from Glauber-Kawasaki dynamics
• Mean curvature interface limit from Glauber+Zero-range interacting particles
• Motion by mean curvature from Glauber-Kawasaki dynamics with speed change
• Stochastic Allen-Cahn equation with mobility
• On large deviations of interface motions for statistical mechanics models
• Lozenge tiling dynamics and convergence to the hydrodynamic equation