Self-similar fragmentations derived from the stable tree I

2003/10/14 by Grégory Miermont, Gregory Marc Miermont
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G52 #msc:60J25 #msc:60J80

paper · pdf · doi:10.1007/s00440-003-0295-x

published as Probability Theory and Related Fields 127 (2003) 423-454 · 30 pages

openalex publication_date 2003/10/14 · arxiv created 2004/05/10 · arxiv updated 2009/12/01 · openalex created_date 2017/03/23 · openalex updated_date 2026/07/29

Abstract

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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