Probability Theory and Related Fields

, Volume 127, Issue 3, pp 423–454 | Cite as

Self-similar fragmentations derived from the stable tree I

  • Grégory Miermont


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.


Self-similar fragmentation stable tree stable process continuous state branching process 


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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.DMA, ENS, et Laboratoire de Probabilités et Modèles aléatoiresUniversité Paris VIParis Cedex 05France

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