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Homogeneous fragmentation processes


Bertoin, Jean (2001). Homogeneous fragmentation processes. Probability Theory and Related Fields, 212(3):301-318.

Abstract

The purpose of this work is to define and study homogeneous fragmentation processes in continuous time, which are meant to describe the evolution of an object that breaks down randomly into pieces as time passes. Roughly, we show that the dynamics of such a fragmentation process are determined by some exchangeable measure on the set of partitions of ℕ, and result from the combination of two different phenomena: a continuous erosion and sudden dislocations. In particular, we determine the class of fragmentation measures which can arise in this setting, and investigate the evolution of the size of the fragment that contains a point picked at random at the initial time.

Abstract

The purpose of this work is to define and study homogeneous fragmentation processes in continuous time, which are meant to describe the evolution of an object that breaks down randomly into pieces as time passes. Roughly, we show that the dynamics of such a fragmentation process are determined by some exchangeable measure on the set of partitions of ℕ, and result from the combination of two different phenomena: a continuous erosion and sudden dislocations. In particular, we determine the class of fragmentation measures which can arise in this setting, and investigate the evolution of the size of the fragment that contains a point picked at random at the initial time.

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Citations

56 citations in Web of Science®
52 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1 November 2001
Deposited On:24 Jul 2013 08:17
Last Modified:07 Dec 2017 21:43
Publisher:Springer
ISSN:0178-8051
Publisher DOI:https://doi.org/10.1007/s004400100152
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1867425
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0992.60076

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