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

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

Regularity of formation of dust in self-similar fragmentations


Code(s) de Classification MSC:

Résumé: In self-similar fragmentations with a negative index, fragments split even faster as their mass is smaller, so that the fragmentation runs away and some mass is reduced to dust. Our purpose is to investigate the regularity of this formation of dust. Let $M(t)$ denote the mass of dust at time $t.\,$We give some sufficient and some necessary conditions for the measure $dM$ to be absolutely continuous. In case of absolute continuity, we obtain an approximation of the density by functions of small fragments. We also study the Hausdorff dimension of the support of $dM$ and the Hölder-continuity of the dust's mass $M$.

Mots Clés: Fragmentation ; self-similarity ; loss of mass to dust ; Lebesgue density ; Hölder-continuity

Date: 2003-06-11

Prépublication numéro: PMA-828