The Annals of Applied Probability

Coexistence in stochastic spatial models

Rick Durrett

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In this paper I will review twenty years of work on the question: When is there coexistence in stochastic spatial models? The answer, announced in Durrett and Levin [Theor. Pop. Biol. 46 (1994) 363–394], and that we explain in this paper is that this can be determined by examining the mean-field ODE. There are a number of rigorous results in support of this picture, but we will state nine challenging and important open problems, most of which date from the 1990’s.

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Ann. Appl. Probab., Volume 19, Number 2 (2009), 477-496.

First available in Project Euclid: 7 May 2009

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Zentralblatt MATH identifier

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

Interacting particle system block construction fast stirring limit competitive exclusion principle


Durrett, Rick. Coexistence in stochastic spatial models. Ann. Appl. Probab. 19 (2009), no. 2, 477--496. doi:10.1214/08-AAP590.

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