A Note on the Probability of Cutting a Galton-Watson Tree
نویسندگان
چکیده
منابع مشابه
A note on the probability of cutting a Galton-Watson tree
The structure of Galton-Watson trees conditioned to be of a given size is wellunderstood. We provide yet another embedding theorem that permits us to obtain asymptotic probabilities of events that are determined by what happens near the root of these trees. As an example, we derive the probability that a Galton-Watson tree is cut when each node is independently removed with probability p, where...
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We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten’s tree. This yields elementary proofs of Kesten’s result as well as other known results on local limit of conditioned Galton-Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton-W...
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Recently, Abraham and Delmas constructed the distributions of super-critical Lévy trees truncated at a fixed height by connecting super-critical Lévy trees to (sub)critical Lévy trees via a martingale transformation. A similar relationship also holds for discrete Galton-Watson trees. In this work, using the existing works on the convergence of contour functions of (sub)critical trees, we prove ...
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Percolation is essentially the study of what happens to a graph when one chooses to remove vertices or edges at random. In particular, one usually chooses some probability, q, and then chooses to remove each edge (or vertex) independently with probability q. We typically study the size and shape of the largest connected component in the remaining graph. We will only study the case in which edge...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2011
ISSN: 1083-6489
DOI: 10.1214/ejp.v16-952