On the Riemann surface type of random planar maps

被引：17

作者：

Gill, James T. ^{[1
]}

Rohde, Steffen ^{[2
]}

机构：

[1] St Louis Univ, Dept Math & Comp Sci, St Louis, MO 63108 USA

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2013年 / 29卷 / 03期

关键词：

Riemann surface; random planar maps; uniformization; SCALING LIMITS;

D O I：

10.4171/RMI/749

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the (random) Riemann surfaces of the Angel Schramm uniform infinite planar triangulation and of Sheffield's infinite necklace construction are both parabolic. In other words, Brownian motion on these surfaces is recurrent. We obtain this result as a corollary to a more general theorem on subsequential distributional limits of random unbiased disc triangulations, following work of Benjamini and Schramm.

引用

页码：1071 / 1090

页数：20

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