The Liouville and the intersection properties are equivalent for planar graphs

Details The Liouville and the intersection properties are equivalent for planar graphs The Liouville and the intersection properties are equivalent for planar graphs

2012-03-18

arxiv.org/abs/1203.4002v1

Mathematics

Probability

4 pages, 1 figure

Scientific paper

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.

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