Asymptotic behavior of edge-reinforced random walks

Details Asymptotic behavior of edge-reinforced random walks Asymptotic behavior of edge-reinforced random walks

2005-11-30

arxiv.org/abs/math/0511750v2

Annals of Probability 2007, Vol. 35, No. 1, 115-140

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000674 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000674

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.

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