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

Dhersin, Jean-Stéphane, Freund, Fabian, Siri-Jégousse, Arno and Yuan, Linglong ORCID: 0000-0002-7851-1631
(2013) On the length of an external branch in the Beta-coalescent. Stochastic Processes and their Applications, 123 (5). pp. 1691-1715.

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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. © 2013 Elsevier B.V. All rights reserved.

Item Type: Article
Uncontrolled Keywords: Coalescent process, Beta-coalescent, External branch, Block counting process, Recursive construction
Depositing User: Symplectic Admin
Date Deposited: 01 Apr 2020 10:52
Last Modified: 18 Jan 2023 23:56
DOI: 10.1016/j.spa.2012.12.010
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3081334