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Broman, E. och Meester, R. (2008) *SURVIVAL OF INHOMOGENEOUS GALTON-WATSON PROCESSES*.

** BibTeX **

@article{

Broman2008,

author={Broman, Erik and Meester, Ronald},

title={SURVIVAL OF INHOMOGENEOUS GALTON-WATSON PROCESSES},

journal={Advances in Applied Probability},

issn={0001-8678},

volume={40},

issue={3},

pages={798-814},

abstract={We study the survival properties of inhomogeneous Galton-Watson processes. We determine the so-called branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which turns out to be an almost sure constant. We also shed some light on the way in which the survival probability varies between the generations. When we perform independent percolation on the family tree of an inhomogeneous Galton-Watson process, the result is essentially a family of inhomogeneous Galton-Watson processes, parameterized by the retention probability p. We provide growth rates, uniformly in p, of the percolation clusters, and also show uniform convergence of the survival probability front the nth level along subsequences. These results also establish, as a corollary, the supercritical continuity of the percolation function. Some of our results are generalizations of results in Lyons (1992).},

year={2008},

keywords={Inhomogeneous Galton-Watson tree, continuity of percolation functions, branching number, RANDOM-WALKS, PERCOLATION, TREES },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 100571

A1 Broman, Erik

A1 Meester, Ronald

T1 SURVIVAL OF INHOMOGENEOUS GALTON-WATSON PROCESSES

YR 2008

JF Advances in Applied Probability

SN 0001-8678

VO 40

IS 3

SP 798

OP 814

AB We study the survival properties of inhomogeneous Galton-Watson processes. We determine the so-called branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which turns out to be an almost sure constant. We also shed some light on the way in which the survival probability varies between the generations. When we perform independent percolation on the family tree of an inhomogeneous Galton-Watson process, the result is essentially a family of inhomogeneous Galton-Watson processes, parameterized by the retention probability p. We provide growth rates, uniformly in p, of the percolation clusters, and also show uniform convergence of the survival probability front the nth level along subsequences. These results also establish, as a corollary, the supercritical continuity of the percolation function. Some of our results are generalizations of results in Lyons (1992).

LA eng

DO 10.1239/aap/1222868186

LK http://dx.doi.org/10.1239/aap/1222868186

OL 30