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A random environment for linearly edge-reinforced random walks on infinite graphs
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  • Published: 06 July 2006

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

  • Franz Merkl1 &
  • Silke W. W. Rolles2 

Probability Theory and Related Fields volume 138, pages 157–176 (2007)Cite this article

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  • 13 Citations

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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.

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Munich, Theresienstr. 39, 80333, Munich, Germany

    Franz Merkl

  2. Zentrum Mathematik, Bereich M5, Technische Universität München, 85747, Garching bei München, Germany

    Silke W. W. Rolles

Authors
  1. Franz Merkl
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  2. Silke W. W. Rolles
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Corresponding author

Correspondence to Silke W. W. Rolles.

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Cite this article

Merkl, F., Rolles, S.W.W. A random environment for linearly edge-reinforced random walks on infinite graphs. Probab. Theory Relat. Fields 138, 157–176 (2007). https://doi.org/10.1007/s00440-006-0016-3

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  • Received: 12 September 2005

  • Revised: 26 April 2006

  • Published: 06 July 2006

  • Issue Date: May 2007

  • DOI: https://doi.org/10.1007/s00440-006-0016-3

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Keywords

  • Reinforced random walk
  • Random environment

Mathematics Subject Classifications (2000)

  • Primary 60K35
  • Secondary 60K37
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