Distances and isoperimetric inequalities in random triangulations of high genus
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Document de travail - Pré-publication
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2023-11-07
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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 ...Leer más >
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.< Leer menos
Proyecto 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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