Open Access
Translator Disclaimer
January 1997 Stochastic models of interacting systems
Thomas M. Liggett
Ann. Probab. 25(1): 1-29 (January 1997). DOI: 10.1214/aop/1024404276


Interacting particle systems is by now a mature area of probability theory, but one that is still very active. We begin this paper by explaining how models from this area arise in fields such as physics and biology. We turn then to a discussion of both older and more recent results about them, concentrating on contact processes, voter models, and exclusion processes. These processes are among the most studied in the field, and have the virtue of relative simplicity in their description, which permits us to address the fundamental issues about their behavior without dealing with the extra complications that models from specific areas of application would require.


Download Citation

Thomas M. Liggett. "Stochastic models of interacting systems." Ann. Probab. 25 (1) 1 - 29, January 1997.


Published: January 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0873.60072
MathSciNet: MR1428497
Digital Object Identifier: 10.1214/aop/1024404276

Primary: 60K35

Keywords: contact processes , Exclusion processes , stochastic Ising model , voter models

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 1 • January 1997
Back to Top