Λ-coalescents: a survey
نویسندگان
چکیده
منابع مشابه
Asymptotic sampling formulae for Λ-coalescents
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Bertoin and Le Gall [1] introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called Λ-coalescent, or coalescent with multiple collisions, introduced independently by Pitman [9] and Sagitov [10]. We show how this process can be extended to the case where linea...
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We consider standard Λ-coalescents (or coalescents with multiple collisions) with a non-trivial “Kingman part”. Equivalently, the driving measure Λ has an atom at 0; Λ({0}) = c > 0. It is known that all such coalescents come down from infinity. Moreover, the number of blocks Nt is asymptotic to v(t) = 2/(ct) as t → 0. In the present paper we investigate the second-order asymptotics of Nt in the...
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We study topological properties of random metric spaces which arise by Λ-coalescents. These are stochastic processes, which start with an infinite number of lines and evolve through multiple mergers in an exchangeable setting. We show that the resulting Λ-coalescent measure tree is compact iff the Λ-coalescent comes down from infinity, i.e. only consists of finitely many lines at any positive t...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2014
ISSN: 0021-9002,1475-6072
DOI: 10.1017/s0021900200021161