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

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.

30 pages

References in corpus (2)

• Ranked Fragmentations
• Self-similar fragmentations derived from the stable tree I: splitting at heights

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