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2012 The Liouville and the intersection properties are equivalent for planar graphs
Itai Benjamini, Nicolas Curien, Agelos Georgakopoulos
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Electron. Commun. Probab. 17: 1-5 (2012). DOI: 10.1214/ECP.v17-1913

Abstract

It is shown that if a planar graph admits no non-constant bounded harmonic function then the trajectories of two independent simple random walks intersect almost surely.

Citation

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Itai Benjamini. Nicolas Curien. Agelos Georgakopoulos. "The Liouville and the intersection properties are equivalent for planar graphs." Electron. Commun. Probab. 17 1 - 5, 2012. https://doi.org/10.1214/ECP.v17-1913

Information

Accepted: 26 September 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1252.05208
MathSciNet: MR2981898
Digital Object Identifier: 10.1214/ECP.v17-1913

Subjects:
Primary: 05C81

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