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April 2009 Coexistence in stochastic spatial models
Rick Durrett
Ann. Appl. Probab. 19(2): 477-496 (April 2009). DOI: 10.1214/08-AAP590

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. "Coexistence in stochastic spatial models." Ann. Appl. Probab. 19 (2) 477 - 496, April 2009. https://doi.org/10.1214/08-AAP590

Information

Published: April 2009
First available in Project Euclid: 7 May 2009

zbMATH: 1178.60069
MathSciNet: MR2521876
Digital Object Identifier: 10.1214/08-AAP590

Subjects:
Primary: 60K35

Keywords: block construction , competitive exclusion principle , fast stirring limit , Interacting particle system

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 2 • April 2009
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