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Scaling Limits of Bipartite Planar Maps are Homeomorphic to the 2-Sphere

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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.

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Authors and Affiliations

  1. Département de Mathématiques, Université Paris-Sud et Institut Uuniversitaire de France, Bâtiment 425, 91405, Orsay Cedex, France

    Jean-François Le Gall

  2. Département de Mathématiques et Applications, UMR 8553 CNRS, Ecole Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Frédéric Paulin

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  1. Jean-François Le Gall
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  2. Frédéric Paulin
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Correspondence to Jean-François Le Gall.

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Received: December 2006, Revision: August 2007, Accepted: October 2007

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Le Gall, JF., Paulin, F. Scaling Limits of Bipartite Planar Maps are Homeomorphic to the 2-Sphere. GAFA Geom. funct. anal. 18, 893–918 (2008). https://doi.org/10.1007/s00039-008-0671-x

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  • DOI: https://doi.org/10.1007/s00039-008-0671-x

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