Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-28T00:20:12.414Z Has data issue: false hasContentIssue false

DISCRETIZATION METHODS FOR HOMOGENEOUS FRAGMENTATIONS

Published online by Cambridge University Press:  20 July 2005

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, Francejbe@ccr.jussieu.fr
ALAIN ROUAULT
Affiliation:
LAMA, Bâtiment Fermat, Université de Versailles, 45 avenue des Etats-Unis, F-78035 Versailles Cedex, Francerouault@math.uvsq.fr
Get access

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

Type
Notes and Papers
Copyright
The London Mathematical Society 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)