An introduction to infinite particle systems

Richard Durrett

Stochastic Processes and their Applications, 1981, vol. 11, issue 2, 109-150

Abstract: In 1970, Spitzer wrote a paper called "Interaction of Markov processes" in which he introduced several classes of interacting particle systems. These processes and other related models, collectively referred to as infinite particle systems, have been the object of much research in the last ten years. In this paper we will survey some of the results which have been obtained and some of the open problems, concentrating on six overlapping classes of processes: the voter model, additive processes, the exponential family, one dimensional systems, attractive systems, and the Ising model.

Keywords: Infinite; particle; system; voter; model; contact; process; additive; process; attractive; system; Ising; model; Gibbs; rate (search for similar items in EconPapers)
Date: 1981
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