Recurrence of edge-reinforced random walk on a two-dimensional graph
Probability
2009-10-13 v2
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 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.
Cite
@article{arxiv.math/0703027,
title = {Recurrence of edge-reinforced random walk on a two-dimensional graph},
author = {Franz Merkl and Silke W. W. Rolles},
journal= {arXiv preprint arXiv:math/0703027},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AOP446 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)