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2013 On the external branches of coalescents with multiple collisions
Jean-Stéphane Dhersin, Martin Möhle
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Electron. J. Probab. 18: 1-11 (2013). DOI: 10.1214/EJP.v18-2286

Abstract

A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Lambda-coalescents) is provided. This recursion is used to derive asymptotic results as the sample size n tends to infinity for the joint moments of the external branch lengths and for the moments of the total external branch length of the Bolthausen-Sznitman coalescent. These asymptotic results are based on a differential equation approach, which is as well useful to obtain exact solutions for the joint moments of the external branch lengths for the Bolthausen-Sznitman coalescent. The results for example show that the lengths of two randomly chosen external branches are positively correlated for the Bolthausen-Sznitman coalescent, whereas they are negatively correlated for the Kingman coalescent provided that n >= 4.

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Jean-Stéphane Dhersin. Martin Möhle. "On the external branches of coalescents with multiple collisions." Electron. J. Probab. 18 1 - 11, 2013. https://doi.org/10.1214/EJP.v18-2286

Information

Accepted: 20 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60079
MathSciNet: MR3040550
Digital Object Identifier: 10.1214/EJP.v18-2286

Subjects:
Primary: 60J25
Secondary: 34E05, 60C05, 60J85, 92D15, 92D25

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