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

   
@article{ECP1583,
	author = {Elie Aidekon},
	title = {Tail asymptotics for the total progeny of the critical killed branching random walk},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {15},
	year = {2010},
	keywords = {Branching random walk, total progeny.},
	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].},
	pages = {no. 47, 522-533},
	issn = {1083-589X},
	doi = {10.1214/ECP.v15-1583},    
        url = {http://ecp.ejpecp.org/article/view/1583}}