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On the total length of external branches for beta-coalescents
- Part of
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- Journal:
- Advances in Applied Probability / Volume 47 / Issue 3 / September 2015
- Published online by Cambridge University Press:
- 21 March 2016, pp. 693-714
- Print publication:
- September 2015
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- Article
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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 nα-1T(n) →DT, 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 limn→+∞n3α-5 𝔼(Lext(n) − n2-α𝔼T)2 = ((α − 1)Γ(α + 1))2Γ(4 − α) / ((3 − α)Γ(4 − 2α)).
of an initial sample of 