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Homogenenous Multitype Fragmentations


Bertoin, Jean (2008). Homogenenous Multitype Fragmentations. In: Sidoravicius, V; Vares, M E. In and Out of Equilibrium 2. Basel: Birkhäuser Basel, 161-183.

Abstract

A homogeneous mass-fragmentation, as it has been defined in [6], describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be enriched by considering also the types of the fragments, where a type may represent, for instance, a geometrical shape, and can take finitely many values. In this setting, the dynamics of a randomly tagged fragment play a crucial role in the analysis of the fragmentation. They are determined by a Markov additive process whose distribution depends explicitly on the characteristics of the fragmentation. As applications, we make explicit the connection with multitype branching random walks, and obtain multitype analogs of the pathwise central limit theorem and large deviation estimates for the empirical distribution of fragments.

A homogeneous mass-fragmentation, as it has been defined in [6], describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be enriched by considering also the types of the fragments, where a type may represent, for instance, a geometrical shape, and can take finitely many values. In this setting, the dynamics of a randomly tagged fragment play a crucial role in the analysis of the fragmentation. They are determined by a Markov additive process whose distribution depends explicitly on the characteristics of the fragmentation. As applications, we make explicit the connection with multitype branching random walks, and obtain multitype analogs of the pathwise central limit theorem and large deviation estimates for the empirical distribution of fragments.

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Additional indexing

Item Type:Book Section, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:29 May 2013 15:22
Last Modified:05 Apr 2016 16:47
Publisher:Birkhäuser Basel
Series Name:Progress in Probability
Number:60
ISBN:978-3-7643-8785-3
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/978-3-7643-8786-0_8
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2477381
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1153.60046
http://arxiv.org/abs/math/0612710
Permanent URL: https://doi.org/10.5167/uzh-78171

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