Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere. (English) Zbl 1166.60006
Summary: 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.
MSC:
60D05 | Geometric probability and stochastic geometry |
05C80 | Random graphs (graph-theoretic aspects) |
53C22 | Geodesics in global differential geometry |
57R30 | Foliations in differential topology; geometric theory |