On Λ-coalescents with dust component

A.V. Gnedin, A. Iksanov, O. Marynych

Research output: Contribution to journalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)1133-1151
Number of pages19
JournalJournal of Applied Probability
Volume48
DOIs
Publication statusPublished - 2011

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