Motion by mean curvature from Glauber-Kawasaki dynamics

Abstract

We study the hydrodynamic scaling limit for the Glauber-Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen-Cahn equation which is a kind of the reaction-diffusion equation in the limit. This paper concerns the scaling that the Glauber part, which governs the creation and annihilation of particles, is also speeded up but slower than the Kawasaki part. Under such scaling, we derive directly from the particle system the motion by mean curvature for the interfaces separating sparse and dense regions of particles as a combination of the hydrodynamic and sharp interface limits.

arXiv comment29 pages

References in corpus (2)

• Mixing times of monotone surfaces and SOS interfaces: a mean curvature approach
• On large deviations of interface motions for statistical mechanics models

Cited by in corpus (5)

• Mean curvature interface limit from Glauber+Zero-range interacting particles
• Motion by mean curvature from Glauber-Kawasaki dynamics with speed change
• Equilibrium perturbations for stochastic interacting systems
• Motion by curvature and large deviations for an interface dynamics on ${\mathbb{Z}}^2$
• Incompressible limit for weakly asymmetric simple exclusion processes coupled through collision