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2008 Bounding a Random Environment Bounding a Random Environment for Two-dimensional Edge-reinforced Random Walk
Franz Merkl, Silke Rolles
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Electron. J. Probab. 13: 530-565 (2008). DOI: 10.1214/EJP.v13-495

Abstract

We consider edge-reinforced random walk on the infinite two-dimensional lattice. The process has the same distribution as a random walk in a certain strongly dependent random environment, which can be described by random weights on the edges. In this paper, we show some decay properties of these random weights. Using these estimates, we derive bounds for some hitting probabilities of the edge-reinforced random walk.

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Franz Merkl. Silke Rolles. "Bounding a Random Environment Bounding a Random Environment for Two-dimensional Edge-reinforced Random Walk." Electron. J. Probab. 13 530 - 565, 2008. https://doi.org/10.1214/EJP.v13-495

Information

Accepted: 12 April 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1187.82051
MathSciNet: MR2399290
Digital Object Identifier: 10.1214/EJP.v13-495

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

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