Geodesic
Ranked fragmentations
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 157-175

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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 the small-time behavior of a ranked fragmentation.

DOI : 10.1051/ps:2002009
Classification : 60J25, 60G09
Keywords: fragmentation, self-similar, subordinator, exchangeable partitions, record process 
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     author = {Berestycki, Julien},
     title = {Ranked fragmentations},
     journal = {ESAIM: Probability and Statistics},
     pages = {157--175},
     publisher = {EDP-Sciences},
     volume = {6},
     year = {2002},
     doi = {10.1051/ps:2002009},
     mrnumber = {1943145},
     zbl = {1001.60078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2002009/}
}
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Berestycki, Julien. Ranked fragmentations. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 157-175. doi: 10.1051/ps:2002009

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