The internal branch lengths of the Kingman coalescent

@article{Dahmer2013TheIB,
  title={The internal branch lengths of the Kingman coalescent},
  author={Iulia Dahmer and G{\"o}tz Kersting},
  journal={arXiv: Probability},
  year={2013}
}
In the Kingman coalescent tree the length of order $r$ is defined as the sum of the lengths of all branches that support $r$ leaves. For $r=1$ these branches are external, while for $r\ge2$ they are internal and carry a subtree with $r$ leaves. In this paper we prove that for any $s\in\mathbb{N}$ the vector of rescaled lengths of orders $1\le r\le s$ converges to the multivariate standard normal distribution as the number of leaves of the Kingman coalescent tends to infinity. To this end we use… 
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