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Displaying similar documents to “Ranked fragmentations”

Ranked Fragmentations

Julien Berestycki (2010)

ESAIM: Probability and Statistics

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In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of these two types of fragmentations. We then give an explicit construction of homogeneous ranked fragmentations in terms of Poisson point processes. Finally we use this construction and classical results on records of Poisson point processes to study...

Small-time behavior of beta coalescents

Julien Berestycki, Nathanaël Berestycki, Jason Schweinsberg (2008)

Annales de l'I.H.P. Probabilités et statistiques

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For a finite measure on [0, 1], the -coalescent is a coalescent process such that, whenever there are clusters, each -tuple of clusters merges into one at rate (1−) (d). It has recently been shown that if 1<<2, the -coalescent in which is the Beta (2−, ) distribution can be used to describe the genealogy of a continuous-state branching process (CSBP) with an -stable branching mechanism. Here...

Alpha-stable branching and beta-coalescents.

Birkner, Matthias, Blath, Jochen, Capaldo, Marcella, Etheridge, Alison M., Möhle, Martin, Schweinsberg, Jason, Wakolbinger, Anton (2005)

Electronic Journal of Probability [electronic only]

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