The Annals of Applied Probability

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.

Article information

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

Dates
First available in Project Euclid: 7 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1241702238

Digital Object Identifier
doi:10.1214/08-AAP590

Mathematical Reviews number (MathSciNet)
MR2521876

Zentralblatt MATH identifier
1178.60069

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

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

Citation

Durrett, Rick. Coexistence in stochastic spatial models. Ann. Appl. Probab. 19 (2009), no. 2, 477--496. doi:10.1214/08-AAP590. https://projecteuclid.org/euclid.aoap/1241702238


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