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November 2005 Edge-reinforced random walk on a ladder
Franz Merkl, Silke W. W. Rolles
Ann. Probab. 33(6): 2051-2093 (November 2005). DOI: 10.1214/009117905000000396


We prove that the edge-reinforced random walk on the ladder ℤ×{1,2} with initial weights a>3/4 is recurrent. The proof uses a known representation of the edge-reinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal of a multicomponent Gibbsian process. A transfer operator technique and entropy estimates from statistical mechanics are used to analyze this Gibbsian process. Furthermore, we prove spatially exponentially fast decreasing bounds for normalized local times of the edge-reinforced random walk on a finite piece of the ladder, uniformly in the size of the finite piece.


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Franz Merkl. Silke W. W. Rolles. "Edge-reinforced random walk on a ladder." Ann. Probab. 33 (6) 2051 - 2093, November 2005.


Published: November 2005
First available in Project Euclid: 7 December 2005

zbMATH: 1102.82010
MathSciNet: MR2184091
Digital Object Identifier: 10.1214/009117905000000396

Primary: 82B41
Secondary: 60K35 , 60K37

Keywords: Gibbs measure , random environment , recurrence , Reinforced random walk , Transfer operator

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • November 2005
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