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In and Out of Equilibrium 2Homogenenous Multitype Fragmentations

In and Out of Equilibrium 2: Homogenenous Multitype Fragmentations [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 2Homogenenous Multitype Fragmentations

Part of the Progress in Probability Book Series (volume 60)
Editors: Sidoravicius, Vladas; Vares, Maria Eulália
Bertoin, Jean
In and Out of Equilibrium 2 — Jan 1, 2008
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References (17)

Publisher
Birkhäuser Basel
Copyright
© Birkhäuser Basel 2008
ISBN
978-3-7643-8785-3
Pages
161 –183
DOI
10.1007/978-3-7643-8786-0_8
Publisher site
See Chapter on Publisher Site

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.]

Published: Jan 1, 2008

Keywords: Multitype; fragmentation; branching process; Markov additive process; 60J80; 60G18

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