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September 2009 Recurrence of edge-reinforced random walk on a two-dimensional graph
Franz Merkl, Silke W. W. Rolles
Ann. Probab. 37(5): 1679-1714 (September 2009). DOI: 10.1214/08-AOP446


We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from ℤ2 by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edge-reinforced random walk on these graphs is recurrent. Furthermore, we derive bounds for the probability that the edge-reinforced random walk hits the boundary of a large box before returning to its starting point.


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Franz Merkl. Silke W. W. Rolles. "Recurrence of edge-reinforced random walk on a two-dimensional graph." Ann. Probab. 37 (5) 1679 - 1714, September 2009.


Published: September 2009
First available in Project Euclid: 21 September 2009

zbMATH: 1180.82085
MathSciNet: MR2561431
Digital Object Identifier: 10.1214/08-AOP446

Primary: 82B41
Secondary: 60K35 , 60K37

Keywords: hitting probabilities , recurrence , Reinforced random walk

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 5 • September 2009
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