On the sphericity of scaling limits of random planar quadrangulations

Details On the sphericity of scaling limits of random planar quadrangulations On the sphericity of scaling limits of random planar quadrangulations

2007-12-21

arxiv.org/abs/0712.3687v1

Mathematics

Probability

11pp, 1 figure

Scientific paper

We give a new proof of a theorem by Le Gall & Paulin, showing that scaling
limits of random planar quadrangulations are homeomorphic to the 2-sphere. The
main geometric tool is a reinforcement of the notion of Gromov-Hausdorff
convergence, called 1-regular convergence, that preserves topological
properties of metric surfaces.

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