Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

The asymptotic behavior of fragmentation processes


Code(s) de Classification MSC:

Résumé: The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the ranked sequence of the masses of the pieces of an object that falls apart randomly as time passes. We investigate their behavior as $t\to\infty$. Roughly, we show that the rate of decay of the $\ell^p$-norm (where $p>1$) is exponential when the index of self-similarity $\alpha$ is $0$, polynomial when $\alpha>0$, whereas the entire mass disappears in a finite time when $\alpha<0$. Moreover, we establish a strong limit theorem for the empirical measure of the fragments in the case when $\alpha>0$. Properties of size-biased picked fragments provide key tools for the study.

Mots Clés: Fragmentation ; self-similar ; scattering rate ; empirical measure

Date: 2001-04-25

Prépublication numéro: PMA-651