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

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

Self-similar fragmentations derived from the stable tree : splitting at heights


Code(s) de Classification MSC:

Résumé: The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process $(F^-(t),t\geq 0)$ out of this tree by removing the vertices located under height $t$. Thanks to a self-similarity property of the stable tree, we show that the fragmentation process is also self-similar. The semigroup and other features of the fragmentation are given explicitly. Asymptotic results are given, as well as a couple of related results on continuous-state branching processes. As proved in a companion paper, another method for fragmenting the stable tree induces another self-similar fragmentation with same characteristics as the ones considered here, except for the speed at which fragments decay.

Mots Clés: Self-similar fragmentation ; stable tree ; stable processes ; continuous-state branching process

Date: 2003-02-26

Prépublication numéro: PMA-796