Asymptotic behavior of edge-reinforced random walks

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

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Probability, Mathematical Physics, 82B41 (Primary) 60K35, 60K37 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/126371

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511750
 http://arxiv.org/abs/math/0511750
 Annals of Probability 2007, Vol. 35, No. 1, 115-140
 doi:10.1214/009117906000000674

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