Distances and isoperimetric inequalities in random triangulations of high genus
hal.structure.identifier | Unité de Mathématiques Pures et Appliquées [UMPA-ENSL] | |
dc.contributor.author | BUDZINSKI, Thomas | |
hal.structure.identifier | Institut de Recherche en Informatique Fondamentale [IRIF (UMR_8243)] | |
dc.contributor.author | CHAPUY, Guillaume | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | BAPTISTE, Louf | |
dc.date.accessioned | 2024-04-04T02:32:36Z | |
dc.date.available | 2024-04-04T02:32:36Z | |
dc.date.created | 2023-11-08 | |
dc.date.issued | 2023-11-07 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190399 | |
dc.description.abstractEn | We 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.sponsorship | Dimères : de la combinatoire à la mécanique quantique - ANR-18-CE40-0033 | |
dc.description.sponsorship | Combinatoire enumerative en interaction avec l'algebre, la theorie des nombres et la physique - ANR-19-CE48-0011 | |
dc.language.iso | en | |
dc.title.en | Distances and isoperimetric inequalities in random triangulations of high genus | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Mathématiques [math] | |
dc.identifier.arxiv | 2311.04005 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-04285094 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-04285094v1 | |
bordeaux.COinS | ctx_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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