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

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 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.

• Publication year

  2012

• Venue

  Stochastic Processes and their Applications

• Publication date

  2012-01-19

• Fields of study

  Biology, Mathematics

• Identifiers
  DOI 10.1016/J.SPA.2012.12.010arXiv 1201.3983
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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