Self-similar fragmentations derived from the stable tree II: splitting at nodes

Details Self-similar fragmentations derived from the stable tree II: splitting at nodes Self-similar fragmentations derived from the stable tree II: splitting at nodes

2004-05-10

arxiv.org/abs/math/0405170v1

Probability Theory and Related Fields 131 (2005) 341--375

Mathematics

Probability

32 pages

Scientific paper

10.1007/s00440-004-0373-8

We study a natural fragmentation process of the so-called stable tree introduced by Duquesne and Le Gall, which consists in removing the nodes of the tree according to a certain procedure that makes the fragmentation self-similar with positive index. Explicit formulas for the semigroup are given, and we provide asymptotic results. We also give an alternative construction of this fragmentation, using paths of Levy processes, hence echoing the two alternative constructions of the standard additive coalescent by fragmenting the Brownian continuum random tree or using Brownian paths, respectively due to Aldous-Pitman and Bertoin.

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