Studies around hydrodynamic limits in interacting particle systems

Abs: Informally, a hydrodynamic limit describes the continuum space-time flow of say mass in a physical system. Making this limit mathematically rigorous has been a constant theme of research in stochastic interacting particle systems going back at least to the 1980’s, with much progress and amazing successes. We will discuss three topics which build on ideas and techniques developed in the course of this study: (1) deriving continuum mean curvature flow from reaction-diffusion type particle systems, (2) nonlinear continuum spde’s as the hydrodynamic limit of particle systems in strong (Sinai-type balanced) random environments, and (3) large deviation limits of a tagged particle in an asymmetric particle system. We will describe recent results, some of their methods, as well as discuss open questions.