The height of the latest common ancestor of two randomly chosen leaves from a (sub-)critical Galton-Watson tree

被引：0

作者：

Huillet, Thierry E. ^{[1
]}

机构：

[1] Univ Cergy Pontoise, CNRS UMR 8089, Lab Phys Theor & Modelisat, Site St Martin,2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise, France

来源：

ADVANCES IN APPLIED MATHEMATICS | 2019年 / 106卷

关键词：

(Sub-)critical Galton-Watson process; Birth and death; Pair coalescence time for two leaves; COALESCENCE TIMES; MODEL;

D O I：

10.1016/j.aam.2019.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Take a complete (sub-)critical Galton-Watson branching tree with finitely many leaves almost surely. Picking two distinct leaves at random, we ask for the height (as measured from the root) of their latest common ancestor. Upon conditioning on the first branching event we compute the distribution of this height, with calculations explicit in the case of a binary tree. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：28 / 36

页数：9

共 3 条

[1] The asymptotic relative generation distribution of the closest common ancestor of the multitype Galton-Watson tree conditioned on non-extinction
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[2] Large and Moderate Deviations for the Total Population Arising from a Sub-critical Galton-Watson Process with Immigration
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[3] Moderate deviations for the total population arising from a nearly unstable sub-critical Galton-Watson process with immigration
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