Compact Brownian surfaces

Vortrag von Prof. Dr. Grégory Miermont

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 27.09.23  Zeit: 17.15 - 18.45  Raum: Y27H12

We describe the compact scaling limits of uniformly random quadrangulations with boundaries on a surface of arbitrary fixed genus. These limits, called Brownian surfaces, are homeomorphic to the surface of the given genus with or without boundaries depending on the scaling regime of the boundary perimeters of the quadrangulation. They are constructed by appropriate gluings of pieces derived from Brownian geometrical objects (the Brownian plane and half-plane). In this talk, I will review their definition and discuss possible alternative constructions. This is based on joint work with Jérémie Bettinelli. ''