Asymptotics of the Hurwitz Binomial Distribution Related to Mixed Poisson Galton–Watson Trees
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Published:2001-05
Issue:3
Volume:10
Page:203-211
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ISSN:0963-5483
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Container-title:Combinatorics, Probability and Computing
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language:en
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Short-container-title:Combinator. Probab. Comp.
Author:
BENNIES JÜRGEN,PITMAN JIM
Abstract
Hurwitz's extension of Abel's binomial theorem defines a probability distribution on the set
of integers from 0 to n. This is the distribution of the number of non-root vertices of a fringe
subtree of a suitably defined random tree with n + 2 vertices. The asymptotic behaviour of
this distribution is described in a limiting regime in which the fringe subtree converges in
distribution to a Galton–Watson tree with a mixed Poisson offspring distribution.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
3 articles.
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1. Computations with Exact Numbers;The Mathematica GuideBook for Numerics;2006
2. Forest Volume Decompositions and Abel–Cayley–Hurwitz Multinomial Expansions;Journal of Combinatorial Theory, Series A;2002-04
3. Invariance Principles for Non-Uniform Random Mappings and Trees;Asymptotic Combinatorics with Application to Mathematical Physics;2002