Journal of Applied Probability

On Λ-coalescents with dust component

Alexander Gnedin, Alexander Iksanov, and Alexander Marynych

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We consider the Λ-coalescent processes with a positive frequency of singleton clusters. The class in focus covers, for instance, the beta(a, b)-coalescents with a > 1. We show that some large-sample properties of these processes can be derived by coupling the coalescent with an increasing Lévy process (subordinator), and by exploiting parallels with the theory of regenerative composition structures. In particular, we discuss the limit distributions of the absorption time and the number of collisions.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 1133-1151.

First available in Project Euclid: 16 December 2011

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 60G09: Exchangeability
Secondary: 60F05: Central limit and other weak theorems 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K05: Renewal theory

Absorption time coupling Lambda-coalescent number of collisions regenerative composition structure subordinator


Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander. On Λ-coalescents with dust component. J. Appl. Probab. 48 (2011), no. 4, 1133--1151. doi:10.1239/jap/1324046023.

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