Limits of the boundary of random planar maps

被引：10
|
作者：
Richier, Loic [1 ]
机构：
[1] Ecole Polytech, CMAP, Palaiseau, France
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2018年 / 172卷 / 3-4期
关键词：
SCALING LIMITS; RANDOM-WALK; TREES;
D O I：
10.1007/s00440-017-0820-y
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 discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter it has a component homeomorphic to the half-plane. As an application, we identify the limits of loops conditioned to be large in the rigid loop model on quadrangulations, proving thereby a conjecture of Curien and Kortchemski.
引用
收藏
页码：789 / 827
页数：39
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