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
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
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