The Annals of Probability

The precise tail behavior of the total progeny of a killed branching random walk

Elie Aïdékon, Yueyun Hu, and Olivier Zindy

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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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Ann. Probab., Volume 41, Number 6 (2013), 3786-3878.

First available in Project Euclid: 20 November 2013

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F05: Central limit and other weak theorems

Killed branching random walk total progeny spinal decomposition Yaglom-type theorem time reversed random walk


Aïdékon, Elie; Hu, Yueyun; Zindy, Olivier. The precise tail behavior of the total progeny of a killed branching random walk. Ann. Probab. 41 (2013), no. 6, 3786--3878. doi:10.1214/13-AOP842.

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