Interacting particle systems - An introduction

Interacting particle systems is a large and growing field of probability theory that is devoted to the rigorous analysis of certain types of models that arise in statistical physics, biology, economics, and other fields. In these notes, we provide an introduction to some of these models, give some basic results about them, and explain how certain important tools are used in their study. The first chapter describes contact, voter and exclusion processes, and introduces the tools of coupling and duality. Chapter 2 is devoted to an analysis of translation invariant linear voter models, using primarily the duality that is available in that case. Chapters 3-5 are concerned with the exclusion process, beginning with the symmetric case, in which one can also use duality, and following with asymmetric systems, which are studied using coupling and other monotonicity techniques. At the end, we report on some very recent work on the stationary distributions of one dimensional systems with positive drift. (author)