An Isaac Newton Institute Programme

Principles of the Dynamics of Non-Equilibrium Systems

Exclusion processes in one and higher dimensions

15th June 2006

Author: Bramson, M (University of Minnesota)

Abstract

Exclusion processes form one of the major classes of interacting particle systems. There, particles on a lattice execute independent random walks in continuous time, except when the target site is already occupied, in which case the particle remains at the original site.

Many results exist for the lattice Z. In particular, the equilibria of such exclusion processes are in many cases well understood. Little is presently known, however, for Z^d, d>1 . We will review the behavior of the exclusion process on Z and with the remaining time present the foundation of a theory for d>1 .