Recurrence of edge-reinforced random walk on a two-dimensional graph
Franz Merkl and Silke W. W. Rolles
Source: Ann. Probab.
Volume 37, Number 5
(2009), 1679-1714.
Abstract
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.
Primary Subjects: 82B41
Secondary Subjects: 60K35, 60K37
Keywords: Reinforced random walk; recurrence; hitting probabilities
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1253539854
Digital Object Identifier: doi:10.1214/08-AOP446
Zentralblatt MATH identifier:
05625050
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