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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
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