Tadahisa Funaki: Interface and its fluctuation in interacting particle systems

We show the separation of particles into sparse and dense phases in Glauber-Kawasaki dynamics of non-gradient type and prove that the interface separating these two regions evolves according to the anisotropic curvature flow. We also study the fluctuation of the interface in a simple situation and derive a stochastic partial differential equation. The results presented at the ICBS last year are extended. The talk is partly based on joint work with Chenlin Gu, Han Wang (Tsinghua University), Hyunjoon Park (Meiji University), Claudio Landim (IMPA), Sunder Sethuraman (University of Arizona) and can be found in arXiv:2404.18364, arXiv:2404.12234, arXiv:2403.01732.