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Pré-Publication, Document De Travail Année : 2023

Distances and isoperimetric inequalities in random triangulations of high genus

Résumé

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.
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Dates et versions

hal-04285094 , version 1 (14-11-2023)

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Thomas Budzinski, Guillaume Chapuy, Louf Baptiste. Distances and isoperimetric inequalities in random triangulations of high genus. 2023. ⟨hal-04285094⟩
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