On the sphericity of scaling limits of random planar quadrangulations
Probability
2008-01-02 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0712.3687,
title = {On the sphericity of scaling limits of random planar quadrangulations},
author = {Grégory Marc Miermont},
journal= {arXiv preprint arXiv:0712.3687},
year = {2008}
}
Comments
11pp, 1 figure