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Ranked fragmentations

Julien Berestycki (2002)

ESAIM: Probability and Statistics

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 the small-time...

Ranked Fragmentations

Julien Berestycki (2010)

ESAIM: Probability and Statistics

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 the small-time behavior...

Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees

Bo Chen, Matthias Winkel (2013)

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

We introduce the notion of a restricted exchangeable partition of ℕ . We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In particular, we deduce from the general theory developed here a limit result conjectured previously for Ford’s alpha model and its extension, the alpha-gamma model, where restricted exchangeability arises naturally.

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