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SURVIVAL OF INHOMOGENEOUS GALTON-WATSON PROCESSES

Erik Broman (Institutionen för matematiska vetenskaper, matematik) ; Ronald Meester
Advances in Applied Probability (0001-8678). Vol. 40 (2008), 3, p. 798-814.
[Artikel, refereegranskad vetenskaplig]

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).

Nyckelord: Inhomogeneous Galton-Watson tree, continuity of percolation functions, branching number, RANDOM-WALKS, PERCOLATION, TREES



Denna post skapades 2009-10-22.
CPL Pubid: 100571

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur