Coexistence in stochastic spatial models
Rick Durrett
Source: Ann. Appl. Probab. Volume 19, Number 2
(2009), 477-496.
Abstract
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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Keywords: Interacting particle system; block construction; fast stirring limit; competitive exclusion principle
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1241702238
Digital Object Identifier: doi:10.1214/08-AAP590
Zentralblatt MATH identifier: 05566088
Mathematical Reviews number (MathSciNet): MR2521876
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