Ranked Fragmentations

Details Ranked Fragmentations Ranked Fragmentations

2006-04-25

arxiv.org/abs/math/0604523v1

ESAIM: P&S, July 2002, Vol. 6, pp. 157-175

Mathematics

Probability

31 pages

Scientific paper

10.1051/ps:2002009

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 of a ranked fragmentation.

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