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1 results

  • On Λ-Coalescents with Dust Component

  • Part of
  • Alexander Gnedin, Alexander Iksanov, Alexander Marynych
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 4 / December 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 1133-1151
    Print publication:
    December 2011
    • Article
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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.