COEXISTENCE IN STOCHASTIC SPATIAL MODELS

• 成果类型: Article
• 署名作者: Durrett, Rick
• 署名单位: Cornell University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP590
• 发表日期: 2009
• 页码: 477-496
• 关键词: surface-reaction model; interspecific competition; catalytic surfaces; particle-systems; host-pathogen; extension; STABILITY

摘要

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.