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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60F25 $L^p$-limit theorems
- 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

**Résumé:** We consider a self-similar fragmentation process in which the
generic particle of mass $x$ is replaced by the offspring particles at
probability rate $x^\alpha$, with positive parameter $\alpha$.
The total of offspring masses may be both larger or smaller than $x$
with positive probability.
We show that under certain conditions the typical mass in the ensemble
is of the order $t^{-1/\alpha}$ and
that the empirical distribution of masses converges to a random limit
which we characterise in terms of the
reproduction law.

**Mots Clés:** *Strong asymptotic laws ; self-similar fragmentation*

**Date:** 2004-02-13

**Prépublication numéro:** *PMA-882*