Regularity of formation of dust in self-similar fragmentations
Bénédicte Haas (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Bénédicte Haas (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Julien Berestycki (2002)
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...
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...
Steven N. Evans, Jim Pitman (1998)
Annales de l'I.H.P. Probabilités et statistiques
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Bertoin, Jean, Pitman, Jim (2000)
Electronic Journal of Probability [electronic only]
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Christina Goldschmidt, Bénédicte Haas (2010)
Annales de l'I.H.P. Probabilités et statistiques
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The stable fragmentation with index of self-similarity ∈[−1/2, 0) is derived by looking at the masses of the subtrees formed by discarding the parts of a (1+)−1–stable continuum random tree below height , for ≥0. We give a detailed limiting description of the distribution of such a fragmentation, ((), ≥0), as it approaches its time of extinction, . In particular, we show that 1/ ((−)+) converges in distribution as →0 to a non-trivial limit. In order to prove this, we go...