Extinction window of mean field branching annihilating random walk

Idan Perl, Arnab Sen, Ariel Yadin

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)3139-3161
Number of pages23
JournalAnnals of Applied Probability
Volume25
Issue number6
DOIs
StatePublished - 1 Dec 2015

Keywords

  • Branching annihilating random walk
  • Branching process
  • Population models

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