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

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

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.

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  • Dhersin, Jean-Stéphane & Freund, Fabian & Siri-Jégousse, Arno & Yuan, Linglong, 2013. "On the length of an external branch in the Beta-coalescent," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1691-1715.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:5:p:1691-1715
    DOI: 10.1016/j.spa.2012.12.010
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    References listed on IDEAS

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    1. Schweinsberg, Jason, 2003. "Coalescent processes obtained from supercritical Galton-Watson processes," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 107-139, July.
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    Cited by:

    1. Disanto, Filippo & Wiehe, Thomas, 2020. "Measuring the external branches of a Kingman tree: A discrete approach," Theoretical Population Biology, Elsevier, vol. 134(C), pages 92-105.

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