Large scale behavior of asymmetric interacting systems in one dimension

Timo Seppalainen University of Wisconsin

Abstract

The typical large scale behavior of an asymmetric particle system is described by a Hamilton-Jacobi equation, in the sense that the random evolution converges to a deterministic solution of such an equation in a space-time scaling limit. This talk describes such limits and the fluctuations from the limit.

It turns out that for asymmetric systems dynamical noise occurs at a scale smaller than the diffusive scale that is common in central limit type results. Specific models from the field of interacting particle systems discussed here are the exclusion process, Hammersley's process, independent random walks, and the random average process.