Asymptotic behavior of edge-reinforced random walks
Merkl, Franz ; Rolles, Silke W. W.
arXiv, 0511750 / Harvested from arXiv
Text on arXiv
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 : 2005-11-30
Classification:  Mathematics - Probability,  Mathematical Physics,  82B41 (Primary) 60K35, 60K37 (Secondary) 
@article{0511750,
     author = {Merkl, Franz and Rolles, Silke W. W.},
     title = {Asymptotic behavior of edge-reinforced random walks},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511750}
}

Merkl, Franz; Rolles, Silke W. W. Asymptotic behavior of edge-reinforced random walks. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511750/