Interacting Particle Systems and Their Scaling Limits

摘要

The primary objective of this project was to understand the long term behavior ofinteracting systems with a large number of components, especially in the presence of one or more conserved quantities. The basic tool that we used in the analysis was the Dirichlet form. For the model known as the Symmetric Simple Exclusion we established the large deviation principle and in the process of completing the above work we developed an improved existence and uniqueness theory for time inhomogeneous diffusion processes with generators in divergence form involving diffusion coefficients that are degenerate and have only minimal smoothness. We established hydrodynamic limit and large deviation estimates for lattice gas models involving Gibbs measures that satisfy mixing conditions. This is a nongradient system and we had to extend the methods developed earlier for product measures to Gibbs measures with mixing conditions.