A stationary planar random graph with singular stationary dual: dyadic lattice graphs
成果类型：
Article
署名作者：
Lyons, Russell; White, Graham
署名单位：
Indiana University System; Indiana University Bloomington
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-019-00934-0
发表日期：
2020
页码：
1011-1043
关键词：
摘要：
Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a singular stationary measure. This answers a question of Curien and shows behaviour different from the unimodular case. The consequence is that planar duality does not combine well with stationary random graphs. We also study harmonic measure on dyadic lattice graphs and show its singularity.