Interacting Particle Systems and Random Media: An Overview

Abstract

Summary We have learned much about spatial random processes during the last 15 years. Physical science is a rich source of interesting questions, some of which have motivated probabilists to develop related mathematical theory. We describe something of two such theories here, concerning interacting particle systems and random media. In the first category, we concentrate on the stochastic Ising model and the exclusion process, and in the second on the percolation process and the question of flows through random media. We attempt to describe the general flavours of these topics, with brief accounts of recent developments and important open problems.