Journal of Applied Probability

A construction of a β-coalescent via the pruning of binary trees

Romain Abraham and Jean-François Delmas

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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.

Article information

Source
J. Appl. Probab., Volume 50, Number 3 (2013), 772-790.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1378401235

Digital Object Identifier
doi:10.1239/jap/1378401235

Mathematical Reviews number (MathSciNet)
MR3102514

Zentralblatt MATH identifier
1285.60078

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Coalescent process binary tree pruning continuum random tree

Citation

Abraham, Romain; Delmas, Jean-François. A construction of a β-coalescent via the pruning of binary trees. J. Appl. Probab. 50 (2013), no. 3, 772--790. doi:10.1239/jap/1378401235. https://projecteuclid.org/euclid.jap/1378401235


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