Clay Mathematics Institute

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Brownian surfaces

Grégory Miermont (ENS Lyon)

Abstract: We show that a random bipartite quadrangulation on a given compact orientable surface rescales, as the number of faces tends to infinity, to an object that can be understood as a Brownian map with the topology specified by the chosen surface. This is achieved by a surgical approach, which consists in cutting the maps along selected geodesics to obtain pieces that can be related to the classical spherical Brownian map.  This is a joint work with Jérémie Bettinelli.