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2010 Tail asymptotics for the total progeny of the critical killed branching random walk
Elie Aidekon
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Electron. Commun. Probab. 15: 522-533 (2010). DOI: 10.1214/ECP.v15-1583

Abstract

We consider a branching random walk on $R$ with a killing barrier at zero. At criticality, the process becomes eventually extinct, and the total progeny $Z$ is therefore finite. We show that $P(Z>n)$ is of order $(n\ln^2(n))^{-1}$, which confirms the prediction of Addario-Berry and Broutin [1].

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Elie Aidekon. "Tail asymptotics for the total progeny of the critical killed branching random walk." Electron. Commun. Probab. 15 522 - 533, 2010. https://doi.org/10.1214/ECP.v15-1583

Information

Accepted: 2 November 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60117
MathSciNet: MR2737710
Digital Object Identifier: 10.1214/ECP.v15-1583

Subjects:
Primary: 60J80

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