Distances and isoperimetric inequalities in random triangulations of high genus
Langue
en
Document de travail - Pré-publication
Ce document a été publié dans
2023-11-07
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Project ANR
Dimères : de la combinatoire à la mécanique quantique - ANR-18-CE40-0033
Combinatoire enumerative en interaction avec l'algebre, la theorie des nombres et la physique - ANR-19-CE48-0011
Combinatoire enumerative en interaction avec l'algebre, la theorie des nombres et la physique - ANR-19-CE48-0011
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