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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 24 open journal systems 


On the sphericity of scaling limits of random planar quadrangulations

Grégory Miermont, Fondation des Sciences Mathématiques de Paris


Abstract
We give a new proof of a theorem by Le Gall and 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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Pages: 248-257

Published on: May 4, 2008


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Electronic Communications in Probability. ISSN: 1083-589X