On the sphericity of scaling limits of random planar quadrangulations

被引：35

作者：

Miermont, Gregory ^{[1
]}

机构：

[1] Univ Paris 06, F-75013 Paris, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2008年 / 13卷

关键词：

random planar maps; scaling limits; Gromov-Hausdorff convergence; spherical topology;

D O I：

10.1214/ECP.v13-1368

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：248 / 257

页数：10

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