Lambda-coalescents with dust component

Abstract

We consider the lambda-coalescent processes with 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 L{é}vy 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.

21 pages

References in corpus (4)

• Asymptotic laws for compositions derived from transformed subordinators
• Limit theorems for the number of occupied boxes in the Bernoulli sieve
• On the number of collisions in beta(2, $b$)-coalescents
• Small parts in the Bernoulli sieve