Tail asymptotics for the total progeny of the critical killed branching random walk

Details Tail asymptotics for the total progeny of the critical killed branching random walk Tail asymptotics for the total progeny of the critical killed branching random walk

2009-11-04

arxiv.org/abs/0911.0877v2

Elec. Com. in Prob. (2010), 15, 522-533

Mathematics

Probability

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Scientific paper

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

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