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On the length of an external branch in the beta-coalescents (2012)
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by
Jean-stéphane Dhersin
,
Fabian Freund
,
Arno Siri-jégousse
,
Linglong Yuan
| Citations: | 4 - 3 self |
BibTeX
@TECHREPORT{Dhersin12onthe,
author = {Jean-stéphane Dhersin and Fabian Freund and Arno Siri-jégousse and Linglong Yuan},
title = {On the length of an external branch in the beta-coalescents},
institution = {},
year = {2012}
}
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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 an external branch of the n-coalescent, we prove the convergence of n α−1 T (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.
