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dc.contributor.authorHaas, Bénédicte
dc.contributor.authorMiermont, Grégory
dc.date.accessioned2010-04-06T07:15:33Z
dc.date.available2010-04-06T07:15:33Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3816
dc.language.isoenen
dc.subjectfragmentation treesen
dc.subjectBrownian treeen
dc.subjectstable treesen
dc.subjectrandom unordered treesen
dc.subjectMarkov branching treesen
dc.subjectscaling limitsen
dc.subject.ddc519en
dc.titleScaling limits of Markov branching trees, with applications to Galton-Watson and random unordered treesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a tree is distributed in its different subtrees. Under some natural assumption on these distributions, stipulating that ``macroscopic'' splitting events are rare, we show that Markov branching trees admit the so-called self-similar fragmentation trees as scaling limits in the Gromov-Hausdorff-Prokhorov topology. Applications include scaling limits of consistent Markov branching model, and convergence of Galton-Watson trees towards the Brownian and stable continuum random trees. We also obtain that random uniform unordered trees have the Brownian tree as a scaling limit, hence extending a result by Marckert-Miermont and fully proving a conjecture made by Aldous.en
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol40
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages2589-2666
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/11-AOP686
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00464337/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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