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.

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