Mathematics – Probability
Scientific paper
2011-12-21
Advances in Applied Probability, 40 (2008), 798-814
Mathematics
Probability
22 pages
Scientific paper
We study 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 a.s.\ constant. We also shed some light on the way 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, parametrized 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 from the $n$-th level along subsequences. These results also establish, as a corollary, the supercritical continuity of the percolation function. Some of our results are generalisations of results by Lyons (1992).
Broman Erik
Meester Ronald
No associations
LandOfFree
Survival of inhomogeneous Galton-Watson processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Survival of inhomogeneous Galton-Watson processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Survival of inhomogeneous Galton-Watson processes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-191503