# zbMATH — the first resource for mathematics

Self-similar fragmentation derived from the stable tree. I: Splitting at heights. (English) Zbl 1042.60043
From the author’s summary: 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.

##### MSC:
 60J25 Continuous-time Markov processes on general state spaces 60G52 Stable stochastic processes 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
Full Text: