ISOPERIMETRIC-INEQUALITIES AND TRANSIENT RANDOM-WALKS ON GRAPHS

• 成果类型: Article
• 署名作者: THOMASSEN, C
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989708
• 发表日期: 1992
• 页码: 1592-1600
• 关键词: riemannian-manifolds

摘要

The two-dimensional grid Z2 and any graph of smaller growth rate is recurrent. We show that any graph satisfying an isoperimetric inequality only slightly stronger than that of Z2 is transient. More precisely, if f(k) denotes the smallest number of vertices in the boundary of a connected subgraph with k vertices, then the graph is transient if the infinite sum SIGMA-f(k)-2 converges. This can be applied to parabolicity versus hyperbolicity of surfaces.