Self-similar fragmentations derived from the stable tree I: splitting at heights
arXiv:math/0405168 · doi:10.1007/s00440-003-0295-x
Abstract
The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process out of this tree by removing the vertices located under height . 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