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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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. © 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 |
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