In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given by random weights on the edges. The edge weights decay exponentially in space. The process converges to a stationary process. We provide asymptotic bounds for the range of the random walker up to a given time, showing that it localizes much more than an ordinary random walker. The random environment is described in terms of an infinite-volume Gibbs measure.
Publié le : 2007-01-14
Classification:
Reinforced random walk,
convergence to equilibrium,
random environment,
Gibbs measure,
82B41,
60K35,
60K37
@article{1174324125,
author = {Merkl, Franz and Rolles, Silke W. W.},
title = {Asymptotic behavior of edge-reinforced random walks},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 115-140},
language = {en},
url = {http://dml.mathdoc.fr/item/1174324125}
}
Merkl, Franz; Rolles, Silke W. W. Asymptotic behavior of edge-reinforced random walks. Ann. Probab., Tome 35 (2007) no. 1, pp. 115-140. http://gdmltest.u-ga.fr/item/1174324125/