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December 2015 Extinction window of mean field branching annihilating random walk
Idan Perl, Arnab Sen, Ariel Yadin
Ann. Appl. Probab. 25(6): 3139-3161 (December 2015). DOI: 10.1214/14-AAP1069


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.


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Idan Perl. Arnab Sen. Ariel Yadin. "Extinction window of mean field branching annihilating random walk." Ann. Appl. Probab. 25 (6) 3139 - 3161, December 2015.


Received: 1 October 2013; Revised: 1 August 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1328.60198
MathSciNet: MR3404633
Digital Object Identifier: 10.1214/14-AAP1069

Primary: 60J80, 92D25

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.25 • No. 6 • December 2015
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