The Annals of Probability

Stochastic models of interacting systems

Thomas M. Liggett

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Abstract

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.

Article information

Source
Ann. Probab., Volume 25, Number 1 (1997), 1-29.

Dates
First available in Project Euclid: 18 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1024404276

Digital Object Identifier
doi:10.1214/aop/1024404276

Mathematical Reviews number (MathSciNet)
MR1428497

Zentralblatt MATH identifier
0873.60072

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
STochastic Ising model contact processes voter models exclusion processes

Citation

Liggett, Thomas M. Stochastic models of interacting systems. Ann. Probab. 25 (1997), no. 1, 1--29. doi:10.1214/aop/1024404276. https://projecteuclid.org/euclid.aop/1024404276


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