On the sphericity of scaling limits of random planar quadrangulations

Grégory Miermont (1, 2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Random planar maps; scaling limits; spherical topoloy

Domaines: Probabilités [math.PR]

Grégory Miermont. On the sphericity of scaling limits of random planar quadrangulations. Electronic Communications in Probability, 2008, 13, pp.248--257. ⟨hal-00200723⟩