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September 2013 A construction of a β-coalescent via the pruning of binary trees
Romain Abraham, Jean-François Delmas
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J. Appl. Probab. 50(3): 772-790 (September 2013). DOI: 10.1239/jap/1378401235

Abstract

Considering a random binary tree with n labelled leaves, we use a pruning procedure on this tree in order to construct a β(3/2,1/2)-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 β-coalescent process up to some time change. These two constructions enable 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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Romain Abraham. Jean-François Delmas. "A construction of a β-coalescent via the pruning of binary trees." J. Appl. Probab. 50 (3) 772 - 790, September 2013. https://doi.org/10.1239/jap/1378401235

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1285.60078
MathSciNet: MR3102514
Digital Object Identifier: 10.1239/jap/1378401235

Subjects:
Primary: 60J25
Secondary: 60J80

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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