Abstract

We discuss the derivation of motion by mean curvature from two types of interacting particle systems, Glauber-Zero range process and Glauber-Kawasaki dynamics with speed change, via hydrodynamic limit. Glauber part of the system controls creation and annihilation of particles, while the other part prescribes the interaction rule for particles performing random walks. Microscopically, the system exhibits a phase separation to sparse and dense regions of particles and, macroscopically, the interface separating these two regions evolves under the MMC . We pass by the Allen-Cahn equation with nonlinear Laplacian at an intermediate level. The so-called Boltzmann-Gibbs principle plays a fundamental role. We also rely on Schauder estimate for quasilinear discrete PDEs. The talk is based on joint works with S. Sethuraman, D. Hilhorst, P. El Kettani and H. Park (arXiv:2004.05276, arXiv:2112.13081), S. Sethuraman (arXiv:2112.13973), P. van Meurs, S. Sethuraman and K. Tsunoda (soon on arXiv).