Géométrie des surfaces browniennes

Appears in collection : Séminaire Poincaré XXIV - Gravité quantique

We discuss the random metric spaces called Brownian surfaces, which arise as scaling limits of large graphs embedded in the sphere or in a surface of higher genus. In particular, we give a detailed construction of the Brownian sphere, and we briefly present recent results of Bettinelli and Miermont concerning Brownian surfaces with holes in higher genus. We also state a few open problems and conjectures.