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Scaling limit of random plane quadrangulations with a simple boundary, via restriction

hal.structure.identifierLaboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
dc.contributor.authorBETTINELLI, Jérémie
dc.contributor.authorCURIEN, Nicolas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorFREDES, Luis
hal.structure.identifierUniversidad de Chile = University of Chile [Santiago] [UCHILE]
dc.contributor.authorSEPÚLVEDA, Avelio
dc.date.accessioned2024-04-04T02:29:50Z
dc.date.available2024-04-04T02:29:50Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190212
dc.description.abstractEnThe main purpose of this work is to provide a framework for proving that, given a family of random maps known to converge in the Gromov--Hausdorff sense, then some (suitable) conditional families of random maps converge to the same limit. As a proof of concept, we show that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence $(p_n)$ of even positive integers with $p_n\sim 2\alpha \sqrt{2n}$ for some $\alpha\in(0,\infty)$. Then, for the Gromov--Hausdorff topology, a quadrangulation with a simple boundary uniformly sampled among those with $n$ inner faces and boundary length $p_n$ weakly converges, in the usual scaling $n^{-1/4}$, toward the Brownian disk of perimeter $3\alpha$.
dc.language.isoen
dc.title.enScaling limit of random plane quadrangulations with a simple boundary, via restriction
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.identifier.arxiv2104.12716
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-03209207
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03209207v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BETTINELLI,%20J%C3%A9r%C3%A9mie&CURIEN,%20Nicolas&FREDES,%20Luis&SEP%C3%9ALVEDA,%20Avelio&rft.genre=preprint


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