Bounding a Random Environment Bounding a Random Environment for Two-dimensional Edge-reinforced Random Walk

Franz Merkl (University of Munich, Germany)
Silke W.W. Rolles (Technical University of Munich)

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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Pages: 530-565

Publication Date: April 12, 2008

DOI: 10.1214/EJP.v13-495

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