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Distances and isoperimetric inequalities in random triangulations of high genus

hal.structure.identifierUnité de Mathématiques Pures et Appliquées [UMPA-ENSL]
dc.contributor.authorBUDZINSKI, Thomas
hal.structure.identifierInstitut de Recherche en Informatique Fondamentale [IRIF (UMR_8243)]
dc.contributor.authorCHAPUY, Guillaume
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBAPTISTE, Louf
dc.date.accessioned2024-04-04T02:32:36Z
dc.date.available2024-04-04T02:32:36Z
dc.date.created2023-11-08
dc.date.issued2023-11-07
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190399
dc.description.abstractEnWe prove that uniform random triangulations whose genus is proportional to their size n have diameter of order log n with high probability. We also show that in such triangulations, the distances between most pairs of points differ by at most an additive constant. Our main tool to prove those results is an isoperimetric inequality of independent interest: any part of the triangulation whose size is large compared to log n has a perimeter proportional to its volume.
dc.description.sponsorshipDimères : de la combinatoire à la mécanique quantique - ANR-18-CE40-0033
dc.description.sponsorshipCombinatoire enumerative en interaction avec l'algebre, la theorie des nombres et la physique - ANR-19-CE48-0011
dc.language.isoen
dc.title.enDistances and isoperimetric inequalities in random triangulations of high genus
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
dc.identifier.arxiv2311.04005
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04285094
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04285094v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-11-07&rft.au=BUDZINSKI,%20Thomas&CHAPUY,%20Guillaume&BAPTISTE,%20Louf&rft.genre=preprint


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