Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 40, 11 pp.
On the external branches of coalescents with multiple collisions
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.
Electron. J. Probab., Volume 18 (2013), paper no. 40, 11 pp.
Accepted: 20 March 2013
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 34E05: Asymptotic expansions 60C05: Combinatorial probability 60J85: Applications of branching processes [See also 92Dxx] 92D15: Problems related to evolution 92D25: Population dynamics (general)
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Dhersin, Jean-Stéphane; Möhle, Martin. On the external branches of coalescents with multiple collisions. Electron. J. Probab. 18 (2013), paper no. 40, 11 pp. doi:10.1214/EJP.v18-2286. https://projecteuclid.org/euclid.ejp/1465064265