@article{9fac3033ac8f409ea013b71371af8115,
title = "The Liouville and the intersection properties are equivalent for planar graphs",
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.",
author = "Itai Benjamini and Nicolas Curien and Agelos Georgakopoulos",
note = "FWF Grant [P-24028-N18]Supported by FWF Grant P-24028-N18.",
year = "2012",
month = sep,
doi = "https://doi.org/10.1214/ECP.v17-1913",
language = "الإنجليزيّة",
volume = "17",
pages = "1--5",
journal = "Electronic Communications in Probability",
issn = "1083-589X",
publisher = "Institute of Mathematical Statistics",
}