On the total length of external branches for beta-coalescents

Dhersin, Jean-Stéphane and Yuan, Linglong (2015) On the total length of external branches for beta-coalescents. Advances in Applied Probability, 47 (3). pp. 693-714.

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Abstract

In this paper we consider the beta(2 − α, α)-coalescents with 1 < α < 2 and study the moments of external branches, in particular, the total external branch length of an initial sample of n individuals. For this class of coalescents, it has been proved that n α-1 T (n) →D T, where T (n) is the length of an external branch chosen at random and T is a known nonnegative random variable. For beta(2 − α, α)-coalescents with 1 < α < 2, we obtain lim n→+∞ n 3α-5

Item Type:	Article
Uncontrolled Keywords:	Coalescent process, beta-coalescent, total external branch length, Fu and Li's statistical test
Depositing User:	Symplectic Admin
Date Deposited:	01 Apr 2020 10:53
Last Modified:	18 Jan 2023 23:56
DOI:	10.1239/aap/1444308878
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3081332