A random environment for linearly edge-reinforced walks on infinite graphs

F. Merkl; S.W.W. Rolles

doi:10.1007/s00440-006-0016-3

A random environment for linearly edge-reinforced walks on infinite graphs

F. Merkl
, S.W.W. Rolles

Research output: Contribution to journal › Article › Academic › peer-review

16 Citations (Scopus)

Abstract

We consider linearly edge-reinforced random walk on an arbitrary locally finite connected graph. It is shown that the process has the same distribution as a mixture of reversible Markov chains, determined by time-independent strictly positive weights on the edges. Furthermore, we prove bounds for the random weights, uniform, among others, in the size of the graph.

Original language	English
Pages (from-to)	157-176
Journal	Probability Theory and Related Fields
Volume	138
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-006-0016-3
Publication status	Published - 2007

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AB - We consider linearly edge-reinforced random walk on an arbitrary locally finite connected graph. It is shown that the process has the same distribution as a mixture of reversible Markov chains, determined by time-independent strictly positive weights on the edges. Furthermore, we prove bounds for the random weights, uniform, among others, in the size of the graph.

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A random environment for linearly edge-reinforced walks on infinite graphs

Abstract

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