منابع مشابه
Cutting down $\mathbf p$-trees and inhomogeneous continuum random trees
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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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 the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bri...
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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...
متن کاملInhomogeneous continuum random trees and the entrance boundary of the additive coalescent
Abstract. Regard an element of the set of ranked discrete distributions := {(x1, x2, . . .) : x1 ≥ x2 ≥ . . . ≥ 0, ∑ i xi = 1} as a fragmentation of unit mass into clusters of masses xi . The additive coalescent is the -valued Markov process in which pairs of clusters of masses {xi, xj }merge into a cluster of mass xi+xj at rate xi+xj . Aldous and Pitman (1998) showed that a version of this pro...
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2017
ISSN: 1350-7265
DOI: 10.3150/16-bej813