The genealogy of self-similar fragmentations with negative index as a continuum random tree

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dc.creatorHaas, Benedicte
dc.creatorMiermont, Gregory
dc.date2004-01-05
dc.date.accessioned2026-07-07T05:04:22Z
dc.date.available2026-07-07T05:04:22Z
dc.descriptionWe encode a certain class of stochastic fragmentation processes, namely self-similar fragmentation processes with a negative index of self-similarity, into a metric family tree which belongs to the family of Continuum Random Trees of Aldous. When the splitting times of the fragmentation are dense near 0, the tree can in turn be encoded into a continuous height function, just as the Brownian Continuum Random Tree is encoded in a normalized Brownian excursion. Under mild hypotheses, we then compute the Hausdorff dimensions of these trees, and the maximal Hölder exponents of the height functions.
dc.identifierhttps://arxiv.org/abs/math/0401028
dc.identifierhttp://arxiv.org/abs/math/0401028
dc.identifierElectronic Journal of Probability 9 (2004) 57-97
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69774
dc.subjectProbability
dc.subject60G18 ; 60J25 ; 60G09
dc.titleThe genealogy of self-similar fragmentations with negative index as a continuum random tree
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