# Motion by mean curvature from Glauber-Kawasaki dynamics

## TL;DR

This paper derives the motion by mean curvature for particle system interfaces under a specific scaling of Glauber-Kawasaki dynamics, extending hydrodynamic limits to include interface evolution in particle systems.

## Contribution

It introduces a new scaling regime where Glauber dynamics is sped up slower than Kawasaki dynamics, leading to a derivation of mean curvature motion from particle systems.

## Key findings

- Derived motion by mean curvature from Glauber-Kawasaki dynamics.
- Extended hydrodynamic limits to interface evolution.
- Connected particle system behavior with geometric interface motion.

## 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.