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

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

2004-05-10

arxiv.org/abs/math/0405168v1

Probability Theory and Related Fields 127 (2003) 423-454

Mathematics

Probability

30 pages

Scientific paper

10.1007/s00440-003-0295-x

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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