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

E.F. Aidékon

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
70 Downloads (Pure)

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 languageEnglish
Pages (from-to)522-533
JournalElectronic Communications in Probability
Volume15
Publication statusPublished - 2010

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