Scaling limits of random Pólya trees
نویسندگان
چکیده
منابع مشابه
A note on the scaling limits of random Pólya trees
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...
متن کاملScaling limits of large random trees
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...
متن کاملScaling limits of Markov branching trees, with applications to Galton-Watson and random unordered trees
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 ...
متن کاملScaling limits of Markov branching trees
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 ...
متن کاملScaling limits of k-ary growing trees
For each integer k ≥ 2, we introduce a sequence of k-ary discrete trees constructed recursively by choosing at each step an edge uniformly among the present edges and grafting on “its middle” k − 1 new edges. When k = 2, this corresponds to a well-known algorithm which was first introduced by Rémy. Our main result concerns the asymptotic behavior of these trees as n becomes large: for all k, th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2017
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-017-0770-4