The total external length of the evolving Kingman coalescent

@article{Dahmer2014TheTE,
  title={The total external length of the evolving Kingman coalescent},
  author={Iulia Dahmer and G. Kersting},
  journal={Probability Theory and Related Fields},
  year={2014},
  volume={167},
  pages={1165-1214}
}
  • Iulia Dahmer, G. Kersting
  • Published 2014
  • Mathematics
  • Probability Theory and Related Fields
  • The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external tree length of the evolving Kingman coalescent and its asymptotic behaviour when the number of leaves of the tree tends to infinity. We show that on the time-scale of the Moran model slowed down by a factor equal to the population size, the (centred and rescaled) external length process converges to a… CONTINUE READING
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