### 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 $(nln2(n))-1$, which confirms the prediction of Addario-Berry and Broutin [1].

Original language | English |
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Pages (from-to) | 522-533 |

Journal | Electronic Communications in Probability |

Volume | 15 |

Publication status | Published - 2010 |

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## Cite this

Aidékon, E. F. (2010). Tail asymptotics for the total progeny of the critical killed branching random walk.

*Electronic Communications in Probability*,*15*, 522-533.