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DISCRETIZATION METHODS FOR HOMOGENEOUS FRAGMENTATIONS

Published online by Cambridge University Press:  20 July 2005

JEAN BERTOIN  and
ALAIN ROUAULT
JEAN BERTOIN
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires and Institut Universitaire de France, Université Pierre et Marie Curie, 175 rue du Chevaleret, F-75013 Paris, [email protected]
ALAIN ROUAULT
Affiliation:
LAMA, Bâtiment Fermat, Université de Versailles, 45 avenue des Etats-Unis, F-78035 Versailles Cedex, [email protected]
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Abstract

Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogues of a certain type of branching random walk, which suggests the use of time-discretization to shift known results from the theory of branching random walks to the fragmentation setting. In particular, this yields interesting information about the asymptotic behaviour of fragmentations.

On the other hand, homogeneous fragmentations can also be investigated using a powerful technique of discretization of space due to Kingman, namely, the theory of exchangeable partitions of $\mathbb{N}$. Spatial discretization is especially well suited to the direct development for continuous times of the conceptual method of probability tilting of Lyons, Pemantle and Peres.

Keywords

60J2560G09
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 91 - 109
Copyright
The London Mathematical Society 2005

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