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arXiv · 0906.2293

Coexistence in stochastic spatial models

Rick Durrett
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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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Rick Durrett. 2009-06-12. Coexistence in stochastic spatial models. https://doi.org/10.1214/08-aap590

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