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January 2007 Asymptotic behavior of edge-reinforced random walks
Franz Merkl, Silke W. W. Rolles
Ann. Probab. 35(1): 115-140 (January 2007). DOI: 10.1214/009117906000000674

Abstract

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.

Citation

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Franz Merkl. Silke W. W. Rolles. "Asymptotic behavior of edge-reinforced random walks." Ann. Probab. 35 (1) 115 - 140, January 2007. https://doi.org/10.1214/009117906000000674

Information

Published: January 2007
First available in Project Euclid: 19 March 2007

zbMATH: 1206.82082
MathSciNet: MR2303945
Digital Object Identifier: 10.1214/009117906000000674

Subjects:
Primary: 82B41
Secondary: 60K35 , 60K37

Keywords: Convergence to equilibrium , Gibbs measure , random environment , Reinforced random walk

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 1 • January 2007
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