The Liouville and the intersection properties are equivalent for planar graphs
Probability
2012-10-08 v2
Abstract
It is shown that if a planar graph admits no non-constant bounded harmonic functions then the trajectories of two independent simple random walks intersect almost surely.
Cite
@article{arxiv.1203.4002,
title = {The Liouville and the intersection properties are equivalent for planar graphs},
author = {Itai Benjamini and Nicolas Curien and Agelos Georgakopoulos},
journal= {arXiv preprint arXiv:1203.4002},
year = {2012}
}
Comments
4 pages, 1 figure