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.
Publié le : 2009-09-15
Classification:
Reinforced random walk,
recurrence,
hitting probabilities,
82B41,
60K35,
60K37
@article{1253539854,
author = {Merkl, Franz and Rolles, Silke W. W.},
title = {Recurrence of edge-reinforced random walk on a two-dimensional graph},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 1679-1714},
language = {en},
url = {http://dml.mathdoc.fr/item/1253539854}
}
Merkl, Franz; Rolles, Silke W. W. Recurrence of edge-reinforced random walk on a two-dimensional graph. Ann. Probab., Tome 37 (2009) no. 1, pp. 1679-1714. http://gdmltest.u-ga.fr/item/1253539854/