The Liouville and the intersection properties are equivalent for planar graphs

Itaı Benjamini, Nicolas Curien, Agelos Georgakopoulos

Type: Article

Publication Date: 2012-01-01

Citations: 13

DOI: https://doi.org/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.

Locations

arXiv (Cornell University) - View - PDF
Warwick Research Archive Portal (University of Warwick) - View - PDF
Electronic Communications in Probability - View - PDF

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+	Uniform spanning forests associated with biased random walks on Euclidean lattices	2018	Zhan Shi Vladas Sidoravičius Song He Longmin Wang Kainan Xiang
+ PDF Chat	Hyperbolic and Parabolic Unimodular Random Maps	2018	Omer Angel Tom Hutchcroft Asaf Nachmias Gourab Ray
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