GEODESICS AND BOUNDED HARMONIC-FUNCTIONS ON INFINITE PLANAR GRAPHS

被引：5

作者：

NORTHSHIELD, S ^{[1
]}

机构：

[1] UNIV ROCHESTER, ROCHESTER, NY 14627 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1991年 / 113卷 / 01期

关键词：

RANDOM WALK; PLANAR GRAPHS; GEODESIC RAYS; HARMONIC FUNCTIONS;

D O I：

10.2307/2048463

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown there that an infinite connected planar graph with a uniform upper bound on vertex degree and rapidly decreasing Green's function (relative to the simple random walk) has infinitely many pairwise finitely-intersecting geodesic rays starting at each vertex. We then demonstrate the existence of nonconstant bounded harmonic functions on the graph.

引用

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页码：229 / 233

页数：5

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