Open Access
November 2013 The precise tail behavior of the total progeny of a killed branching random walk
Elie Aïdékon, Yueyun Hu, Olivier Zindy
Ann. Probab. 41(6): 3786-3878 (November 2013). DOI: 10.1214/13-AOP842


Consider a branching random walk on the real line with a killing barrier at zero: starting from a nonnegative point, particles reproduce and move independently, but are killed when they touch the negative half-line. The population of the killed branching random walk dies out almost surely in both critical and subcritical cases, where by subcritical case we mean that the rightmost particle of the branching random walk without killing has a negative speed, and by critical case, when this speed is zero. We investigate the total progeny of the killed branching random walk and give their precise tail distribution both in the critical and subcritical cases, which solves an open problem of Aldous [Power laws and killed branching random walks,].


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Elie Aïdékon. Yueyun Hu. Olivier Zindy. "The precise tail behavior of the total progeny of a killed branching random walk." Ann. Probab. 41 (6) 3786 - 3878, November 2013.


Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1288.60105
MathSciNet: MR3161464
Digital Object Identifier: 10.1214/13-AOP842

Primary: 60F05 , 60J80

Keywords: killed branching random walk , spinal decomposition , time reversed random walk , Total progeny , Yaglom-type theorem

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • November 2013
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