Self-similar fragmentations derived from the stable tree I: splitting at heights
Gregory Marc Miermont
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.
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