Journal of Applied Probability

On Λ-coalescents with dust component

Alexander Gnedin, Alexander Iksanov, and Alexander Marynych

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Abstract

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

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

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046023

Digital Object Identifier
doi:10.1239/jap/1324046023

Mathematical Reviews number (MathSciNet)
MR2896672

Zentralblatt MATH identifier
1242.60077

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.jap/1324046023


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