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

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

2006-12-12

arxiv.org/abs/math/0612315v2

Mathematics

Probability

22 pages Second version with minor typographical correction

Scientific paper

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.

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