On Λ-Coalescents with Dust Component

@article{Gnedin2011OnW,
title={On $\Lambda$-Coalescents with Dust Component},
author={Alexander V. Gnedin and Alexander Iksanov and Alexander Marynych},
journal={Journal of Applied Probability},
year={2011},
volume={48},
pages={1133 - 1151}
}
• Published 1 December 2011
• Mathematics, Physics
• Journal of Applied Probability
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…

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