EXTINCTION WINDOW OF MEAN FIELD BRANCHING ANNIHILATING RANDOM WALK

• 成果类型: Article
• 署名作者: Perl, Idan; Sen, Arnab; Yadin, Ariel
• 署名单位: Ben-Gurion University of the Negev; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1069
• 发表日期: 2015
• 页码: 3139-3161
• 关键词: convergence

摘要

We study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are annihilated. This is a nonmonotone model, which makes the analysis more difficult. We consider the extinction window of this model in the finite mean-field case, where there are n sites but movement is allowed to any site (the complete graph). We show that although the system survives for exponential time, the extinction window is logarithmic.