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Scaling Limits of Bipartite Planar Maps are Homeomorphic to the 2-Sphere |
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| Authors: | Jean-François Le Gall Frédéric Paulin |
| Institution: | (1) Département de Mathématiques, Université Paris-Sud et Institut Uuniversitaire de France, Batiment 425, 91405 Orsay Cedex, France;(2) Département de Mathématiques et Applications, UMR 8553 CNRS, Ecole Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France |
| 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. Received: December 2006, Revision: August 2007, Accepted: October 2007 |
| Keywords: | and phrases:" target="_blank"> and phrases: Random planar map scaling limit geodesic lamination random tree Brownian snake |
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