On the absence of percolation in a line-segment based lilypond model

被引:5
|
作者
Hirsch, Christian [1 ]
机构
[1] Univ Ulm, Inst Stochast, D-89069 Ulm, Germany
来源
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2016年 / 52卷 / 01期
关键词
Lilypond model; Mass-transport principle; Percolation; Random geometric graph; Sprinkling;
D O I
10.1214/14-AIHP638
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 prove the absence of percolation in a directed Poisson-based random geometric graph with out-degree 1. This graph is an anisotropic variant of a line-segment based lilypond model obtained from an asymmetric growth protocol, which has been proposed by Daley and Last. In order to exclude backward percolation, one may proceed as in the lilypond model of growing disks and apply the mass-transport principle. Concerning the proof of the absence of forward percolation, we present a novel argument that is based on the method of sprinkling.
引用
收藏
页码:127 / 145
页数:19
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