On the length of an external branch in the Beta-coalescent

Jean-Stéphane Dhersin, Fabian Freund, Arno Siri-Jégousse and Linglong Yuan

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1691-1715

Abstract: In this paper, we consider Beta(2−α,α) (with 1<α<2) and related Λ-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nα−1T(n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent.

Keywords: Coalescent process; Beta-coalescent; External branch; Block counting process; Recursive construction (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:5:p:1691-1715

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DOI: 10.1016/j.spa.2012.12.010

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