Limits of random trees
نویسندگان
چکیده
منابع مشابه
Local limits of random trees and maps
These pages form the lecture notes of a mini-course given at the IXth Young European Probabilists conference that took place in Eindhoven (March 2012). They contain some material extracted from [2, 8, 9]. We survey some aspects of local limits of random trees and maps and deal in particular with the so-called geometric Galton-Watson tree conditioned to survive and the uniform infinite planar qu...
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The goal of these lectures is to survey some of the recent progress on the description of largescale structure of random trees. We will use the framework of Markov branching sequences of trees and develop several applications, to combinatorial trees, Galton-Watson trees, some dynamical models of randomly growing trees, cut trees, etc. This is a rough draft – to be completed – all comments are w...
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Panagiotou and Stufler (arXiv:1502.07180v2) recently proved one important fact on their way to establish the scaling limits of random Pólya trees: a uniform random Pólya tree of size n consists of a conditioned critical Galton-Watson tree Tn and many small forests, where with probability tending to one as n tends to infinity, each forest Fn(v) is maximally of size |Fn(v)| = O(log n). Their proo...
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We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a ...
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2013
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-013-0321-0