Stochastic Interacting Systems: Contact, Voter and Exclusion Processes / Edition 1

by Thomas M. Liggett

Overview

Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics.

Product Details

ISBN-13:	9783540659952
Publisher:	Springer Berlin Heidelberg
Publication date:	10/14/1999
Series:	Grundlehren der mathematischen Wissenschaften , #324
Edition description:	1999
Pages:	335
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Background and Tools.- Contact Processes: Preliminaries; The Process on the Integer Lattice Zd; The Process on (1,...,N)d; The Process on the Homogeneous Tree Td; Notes and References.- Voter Models: Preliminaries; Models with General Threshold and Range; Models with Threshold = 1; Notes and References.- Exclusion Processes: Preliminaries; Asymmetric Processes on the Integers; Invariant Measures for Processes on (1,..,N); The Tagged Particle Process.- Notes and References Bibliography.- Index.