# Talk

Modul:   MAT971  Stochastische Prozesse

## Local limits of uniform triangulations in high genus

Thomas Budzinski talk

Speaker invited by: Prof. Dr. Jean Bertoin

Date: 03.04.19  Time: 17.15 - 19.00  Room: Y27H12

We study the local limits of uniform triangulations chosen uniformly over those with fixed size and genus in the regime where the genus is proportional to the size. We show that they converge to the Planar Stochastic Hyperbolic Triangulations introduced by Curien. This generalizes the convergence of uniform planar triangulations to the UIPT of Angel and Schramm, and proves a conjecture of Benjamini and Curien. As a consequence, we obtain new asymptotics on the enumeration of high genus triangulations. This is a joint work with Baptiste Louf.