Hydrodynamic Limit and Stochastic PDEs Related to Interface Motion

Explore a 45-minute lecture on hydrodynamic limits and stochastic partial differential equations (PDEs) related to interface motion. Delve into various interacting particle systems at the microscopic level, examining how particles move through random walks with or without creation and annihilation. Discover how these systems, through hydrodynamic space-time scaling limits or nonlinear fluctuation limits, lead to three macroscopic phenomena: motion by mean curvature in phase separation, Stefan free boundary problem in species segregation, and coupled Kardar-Parisi-Zhang (KPZ) equations as singular stochastic PDEs. Learn about the crucial role of the Boltzmann-Gibbs principle in these processes and gain insights into the discrete Schauder estimate. Access accompanying slides for visual support of the concepts presented in this International Mathematical Union talk by Tadahisa Funaki.