Coexistence in stochastic spatial models

Details Coexistence in stochastic spatial models Coexistence in stochastic spatial models

2009-06-12

arxiv.org/abs/0906.2293v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 477-496

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP590 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP590

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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