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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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

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

First available in Project Euclid: 5 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Coalescent process binary tree pruning continuum random tree


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.

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