Cutting down trees with a Markov chainsaw
نویسندگان
چکیده
منابع مشابه
Cutting down trees with a Markov chainsaw
We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton–Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny n. Our proof is based on a coupling which yields a precise, non-asymptotic distributional result for the case of uniformly random rooted labeled trees (or, equivalently, Poisson Galto...
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In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...
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We study a fragmentation of the p-trees of Camarri and Pitman [Elect. J. Probab., vol. 5, pp. 1–18, 2000]. We give exact correspondences between the p-trees and trees which encode the fragmentation. We then use these results to study the fragmentation of the ICRTs (scaling limits of p-trees) and give distributional correspondences between the ICRT and the tree encoding the fragmentation. The th...
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Here we consider two parameters for random non-crossing trees: i the number of random cuts to destroy a sizen non-crossing tree and ii the spanning subtree-size of p randomly chosen nodes in a size-n non-crossing tree. For both quantities, we are able to characterise for n ∞ the limiting distributions. Non-crossing trees are almost conditioned Galton-Watson trees, and it has been already shown,...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2014
ISSN: 1050-5164
DOI: 10.1214/13-aap978