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 Electronic Communications in Probability > Vol. 15(2010) > Paper 47 open journal systems 


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

Elie E.F. Aidekon, Technische Universiteit Eindhoven


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].


Full text: PDF

Pages: 522-533

Published on: November 2, 2010
Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X