The CRT is the scaling limit of random dissections
hal.structure.identifier | ||
dc.contributor.author | Curien, Nicolas | * |
hal.structure.identifier | CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] | |
dc.contributor.author | Haas, Bénédicte | * |
hal.structure.identifier | ||
dc.contributor.author | Kortchemski, Igor
HAL ID: 738901 | * |
dc.date.accessioned | 2013-05-23T07:24:30Z | |
dc.date.available | 2013-05-23T07:24:30Z | |
dc.date.issued | 2015 | |
dc.identifier.issn | 1042-9832 | |
dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/11289 | |
dc.language.iso | en | en |
dc.subject | Brownian Continuum Random Tree | |
dc.subject | Gromov–Hausdorff topology | |
dc.subject | Random dissections | |
dc.subject | Galton–Watson trees | |
dc.subject | scaling limits | |
dc.subject.ddc | 519 | en |
dc.title | The CRT is the scaling limit of random dissections | |
dc.type | Article accepté pour publication ou publié | |
dc.contributor.editoruniversityother | Département de Mathématiques et Applications (DMA) http://www.dma.ens.fr/ CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris;France | |
dc.contributor.editoruniversityother | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) http://www.proba.jussieu.fr/ CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot;France | |
dc.description.abstracten | We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform $p$-angulations. As their number of vertices $n$ goes to infinity, we show that these random graphs, rescaled by $n^{-1/2}$, converge in the Gromov--Hausdorff sense towards a multiple of Aldous' Brownian tree when the weights decrease sufficiently fast. The scaling constant depends on the Boltzmann weights in a rather amusing and intriguing way, and is computed by making use of a Markov chain which compares the length of geodesics in dissections with the length of geodesics in their dual trees. | |
dc.relation.isversionofjnlname | Random Structures & Algorithms | |
dc.relation.isversionofjnlvol | 47 | |
dc.relation.isversionofjnlissue | 2 | |
dc.relation.isversionofjnldate | 2015 | |
dc.relation.isversionofjnlpages | 304-327 | |
dc.relation.isversionofdoi | 10.1002/rsa.20554 | |
dc.identifier.urlsite | https://arxiv.org/abs/1305.3534v2 | |
dc.relation.isversionofjnlpublisher | J. Wiley | |
dc.subject.ddclabel | Probabilités et mathématiques appliquées | en |
dc.relation.forthcomingprint | oui | |
dc.description.submitted | non | en |
dc.description.ssrncandidate | non | |
dc.description.halcandidate | oui | |
dc.description.readership | recherche | |
dc.description.audience | International | |
dc.relation.Isversionofjnlpeerreviewed | oui | |
dc.date.updated | 2016-09-16T14:21:23Z | |
hal.author.function | aut | |
hal.author.function | aut | |
hal.author.function | aut |
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