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.

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

References in corpus (4)

• 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