# 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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https://hal.archives-ouvertes.fr/hal-00711518
Contributor : Romain Abraham <>
Submitted on : Friday, November 9, 2012 - 2:16:41 PM
Last modification on : Friday, May 4, 2018 - 1:17:28 AM
Document(s) archivé(s) le : Sunday, February 10, 2013 - 3:42:13 AM

### Files

coalescent_11_12.pdf
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### Identifiers

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

### Citation

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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