Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent

@inproceedings{Drmota2007AsymptoticRC,
  title={Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent},
  author={Michael Drmota and Alexander Iksanov and Martin Moehle and Uwe Roesler},
  year={2007}
}
We study the total branch length Ln of the Bolthausen–Sznitman coalescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown that Ln/E(Ln) converges to 1 in probability and that Ln , properly normalized, converges weakly to a stable random variable as n tends to infinity. The results are applied to derive a corresponding limiting law for the total number of mutations for the Bolthausen–Sznitman coalescent with mutation rate r > 0… CONTINUE READING
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