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

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dc.creatorMiermont, Gregory Marc
dc.date2004-05-10
dc.date.accessioned2026-07-07T05:08:05Z
dc.date.available2026-07-07T05:08:05Z
dc.descriptionThe 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.
dc.description30 pages
dc.identifierhttps://arxiv.org/abs/math/0405168
dc.identifierhttp://arxiv.org/abs/math/0405168
dc.identifierProbability Theory and Related Fields 127 (2003) 423-454
dc.identifierdoi:10.1007/s00440-003-0295-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71119
dc.subjectProbability
dc.subject60J25 ; 60G52 ; 60J80
dc.titleSelf-similar fragmentations derived from the stable tree I: splitting at heights
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