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The Total External Branch Length of Beta-Coalescents†

The Total External Branch Length of Beta-Coalescents† For 1 < α < 2 we derive the asymptotic distribution of the total length of external branches of a Beta(2 − α, α)-coalescent as the number n of leaves becomes large. It turns out that the fluctuations of the external branch length follow those of τn2−α over the entire parameter regime, where τn denotes the random number of coalescences that bring the n lineages down to one. This is in contrast to the fluctuation behaviour of the total branch length, which exhibits a transition at $\alpha_0 = (1+\sqrt 5)/2$ ([18]). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Combinatorics,Probability and Computing" Cambridge University Press

The Total External Branch Length of Beta-Coalescents†

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Publisher
Cambridge University Press
Copyright
Copyright © Cambridge University Press 2014 
ISSN
1469-2163
eISSN
0963-5483
DOI
10.1017/S0963548314000297
Publisher site
See Article on Publisher Site

Abstract

For 1 < α < 2 we derive the asymptotic distribution of the total length of external branches of a Beta(2 − α, α)-coalescent as the number n of leaves becomes large. It turns out that the fluctuations of the external branch length follow those of τn2−α over the entire parameter regime, where τn denotes the random number of coalescences that bring the n lineages down to one. This is in contrast to the fluctuation behaviour of the total branch length, which exhibits a transition at $\alpha_0 = (1+\sqrt 5)/2$ ([18]).

Journal

"Combinatorics,Probability and Computing"Cambridge University Press

Published: Jul 10, 2014

Keywords: Primary 60K35; Secondary 60F05; 60J10

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