Self-similar fragmentations derived from the stable tree I

Abstract

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≥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.