The Continuum Random Tree. I
نویسندگان
چکیده
منابع مشابه
Record Process on the Continuum Random Tree
Abstract. By considering a continuous pruning procedure on Aldous’s Brownian tree, we construct a random variable Θ which is distributed, conditionally given the tree, according to the probability law introduced by Janson as the limit distribution of the number of cuts needed to isolate the root in a critical Galton-Watson tree. We also prove that this random variable can be obtained as the a.s...
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1 INTRODUCTION Many different models of random trees have arisen in a variety of applied setting, and there is a large but scattered literature on exact and asymptotic results for particular models. For several years I have been interested in what kinds of "general theory" (as opposed to ad hoc analysis of particular models) might be useful in studying asymptotics of random trees. In this paper...
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Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated Lévy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using Lévy snake techniques. We then prove that the resulting sub-tree after pruning is still a Lévy continuum random tree. This last result is proved using the exploration process that codes...
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متن کاملFluctuations for the Number of Records on Subtrees of the Continuum Random Tree
We study the asymptotic behavior af the number of cuts X(Tn) needed to isolate the root in a rooted binary random tree Tn with n leaves. We focus on the case of subtrees of the Continuum Random Tree generated by uniform sampling of leaves. We elaborate on a recent result by Abraham and Delmas, who showed that X(Tn)/ √ 2n converges a.s. towards a Rayleigh-distributed random variable Θ, which giv...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1991
ISSN: 0091-1798
DOI: 10.1214/aop/1176990534