Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 3 (2013), 772-790.
A construction of a β-coalescent via the pruning of binary trees
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.
J. Appl. Probab., Volume 50, Number 3 (2013), 772-790.
First available in Project Euclid: 5 September 2013
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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