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The Liouville and the intersection properties are equivalent for planar graphs
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Benjamini, Itai, Curien, Nicolas and Georgakopoulos, Agelos (2012) The Liouville and the intersection properties are equivalent for planar graphs. Electronic communications in probability, Vol.17 . Article no. 42. doi:10.1214/ECP.v17-1913 ISSN 1083-589X.
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Official URL: http://dx.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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Graph theory | ||||
Journal or Publication Title: | Electronic communications in probability | ||||
Publisher: | University of Washington. Dept. of Mathematics | ||||
ISSN: | 1083-589X | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.17 | ||||
Page Range: | Article no. 42 | ||||
DOI: | 10.1214/ECP.v17-1913 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 23 December 2015 | ||||
Date of first compliant Open Access: | 23 December 2015 |
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