Random Recursive Trees and the Bolthausen-Sznitman Coalesent

@article{Goldschmidt2005RandomRT,
  title={Random Recursive Trees and the Bolthausen-Sznitman Coalesent},
  author={Christina Goldschmidt and James B. Martin},
  journal={Electronic Journal of Probability},
  year={2005},
  volume={10},
  pages={718-745}
}
We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to $[n]$: we show that the distribution of the number of blocks involved in the final collision converges as $n\to\infty$, and obtain a scaling law for the sizes of these blocks. We also consider the discrete-time Markov chain giving the number of blocks after each collision… 

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