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Homogeneous fragmentation processes
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  • Published: November 2001

Homogeneous fragmentation processes

  • Jean Bertoin1 

Probability Theory and Related Fields volume 121, pages 301–318 (2001)Cite this article

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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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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires et Institut Universitaire de France, Université Pierre et Marie Curie, et C.N.R.S. UMR 7599, 175, rue du Chevaleret, F-75013 Paris, France. e-mail: jbe@ccr.jussieu.fr, , , , , , FR

    Jean Bertoin

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  1. Jean Bertoin
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Received: 25 April 2000 / Revised version: 1 February 2001 / Published online: 23 August 2001

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Bertoin, J. Homogeneous fragmentation processes. Probab Theory Relat Fields 121, 301–318 (2001). https://doi.org/10.1007/s004400100152

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  • Issue Date: November 2001

  • DOI: https://doi.org/10.1007/s004400100152

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Keywords

  • Initial Time
  • Continuous Time
  • Time Pass
  • Fragmentation Process
  • Fragmentation Measure
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