A construction of a $\beta$-coalescent via the pruning of Binary Trees

Abstract : Considering a random binary tree with $n$ labelled leaves, we use a pruning procedure on this tree in order to construct a $\beta(\frac{3}{2},\frac{1}{2})$-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous's continuum random tree, to construct a continuous state space process that has the same structure as the $\beta$-coalescent process up to some time change. These two constructions unable us to obtain results on the coalescent process such as the asymptotics on the number of coalescent events or the law of the blocks involved in the last coalescent event.
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Article dans une revue
Journal of Applied Probability, Applied Probability Trust, 2013, 50 (3), pp.772-790
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https://hal.archives-ouvertes.fr/hal-00711518
Contributeur : Romain Abraham <>
Soumis le : vendredi 9 novembre 2012 - 14:16:41
Dernière modification le : vendredi 4 mai 2018 - 01:17:28
Document(s) archivé(s) le : dimanche 10 février 2013 - 03:42:13

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coalescent_11_12.pdf
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  • HAL Id : hal-00711518, version 2
  • ARXIV : 1206.5629

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Romain Abraham, Jean-François Delmas. A construction of a $\beta$-coalescent via the pruning of Binary Trees. Journal of Applied Probability, Applied Probability Trust, 2013, 50 (3), pp.772-790. 〈hal-00711518v2〉

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