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Ranked Fragmentations

Published online by Cambridge University Press:  15 November 2002

Julien Berestycki
Julien Berestycki*
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, UMR 7599 du CNRS, 175 rue du Chevaleret, 75013 Paris, France; jberest@ccr.jussieu.fr.
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Abstract

In this paper we define and study self-similar rankedfragmentations. We first show that any ranked fragmentation is theimage of some partition-valued fragmentation, and that there is infact a one-to-one correspondence between the laws of these twotypes of fragmentations. We then give an explicit construction ofhomogeneous ranked fragmentations in terms of Poisson pointprocesses. Finally we use this construction and classical resultson records of Poisson point processes to study the small-timebehavior of a ranked fragmentation.

Keywords

Fragmentationself-similarsubordinatorexchangeablepartitionsrecord process.

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