Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere

Abstract

We prove that scaling limits of random planar maps which are uniformly distributed over the set of all rooted 2k-angulations are a.s. homeomorphic to the two-dimensional sphere. Our methods rely on the study of certain random geodesic laminations of the disk.

22 pages Second version with minor typographical correction

References in corpus (1)

• The topological structure of scaling limits of large planar maps

Cited by in corpus (3)

• The topological structure of scaling limits of large planar maps
• Statistics of geodesics in large quadrangulations
• Toric origami structures on quasitoric manifolds