A study of large fringe and non-fringe subtrees in conditional Galton-Watson trees

We study the conditions for families of subtrees to exist with high probability (whp) in a Galton-Walton tree of size \(n\). We first give a Poisson approximation of fringe subtree counts, which yields the height of the maximal complete \(r\)-ary fringe subtree. Then we determine the maximal \(K_n\)...

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Bibliographic Details
Published inarXiv.org
Main Authors Xing Shi Cai, Devroye, Luc
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.02.2016
Subjects
Height
Mathematics - Probability
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Summary:We study the conditions for families of subtrees to exist with high probability (whp) in a Galton-Walton tree of size \(n\). We first give a Poisson approximation of fringe subtree counts, which yields the height of the maximal complete \(r\)-ary fringe subtree. Then we determine the maximal \(K_n\) such that every tree of size at most \(K_n\) appears as fringe subtree whp. Finally, we study non-fringe subtree counts and determine the height of the maximal complete \(r\)-ary non-fringe subtree.
ISSN:2331-8422
DOI:10.48550/arxiv.1602.03850