The Liouville and the intersection properties are equivalent for planar graphs

Agelos Georgakopoulos; Itai Benjamini; Nicolas Curien

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The Liouville and the intersection properties are equivalent for planar graphs

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arxiv 1203.4002 v2 pith:YBL6LM7S submitted 2012-03-18 math.PR

Itai Benjamini , Nicolas Curien , Agelos Georgakopoulos This is my paper · ORCID

classification math.PR

keywords planaradmitsalmostboundedequivalentfunctionsgraphgraphs

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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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