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

共 50 条

[21] Scaling Limits of Planar Symplectic Ensembles
Akemann, Gernot
Byun, Sung-Soo
Kang, Nam-Gyu
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2022, 18
[22] SCALING LIMITS FOR A RANDOM BOXES MODEL
Aurzada, F.
Schwinn, S.
ADVANCES IN APPLIED PROBABILITY, 2019, 51 (03) : 773 - 801
[23] Scaling limits of random Polya trees
Panagiotou, Konstantinos
Stufler, Benedikt
PROBABILITY THEORY AND RELATED FIELDS, 2018, 170 (3-4) : 801 - 820
[24] SCALING LIMITS FOR ASSOCIATED RANDOM MEASURES
BURTON, R
WAYMIRE, E
ANNALS OF PROBABILITY, 1985, 13 (04): : 1267 - 1278
[25] Limits of the boundary of random planar maps
Richier, Loic
PROBABILITY THEORY AND RELATED FIELDS, 2018, 172 (3-4) : 789 - 827
[26] Limits of the boundary of random planar maps
Loïc Richier
Probability Theory and Related Fields, 2018, 172 : 789 - 827
[27] Scaling limits for planar aggregation with subcritical fluctuations
Norris, James
Silvestri, Vittoria
Turner, Amanda
PROBABILITY THEORY AND RELATED FIELDS, 2023, 185 (1-2) : 185 - 250
[28] Scaling limits for planar aggregation with subcritical fluctuations
James Norris
Vittoria Silvestri
Amanda Turner
Probability Theory and Related Fields, 2023, 185 : 185 - 250
[29] Uniform infinite planar quadrangulations with a boundary
Curien, Nicolas
Miermont, Gregory
RANDOM STRUCTURES & ALGORITHMS, 2015, 47 (01) : 30 - 58
[30] Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: Cone times
Gwynne, Ewain
Mao, Cheng
Sun, Xin
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2019, 55 (01): : 1 - 60

← 1 2 3 4 5 →