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Once edge-reinforced random walk on a tree
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  • Published: April 2002

Once edge-reinforced random walk on a tree

  • Rick Durrett1,
  • Harry Kesten1 &
  • Vlada Limic1 

Probability Theory and Related Fields volume 122, pages 567–592 (2002)Cite this article

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  • 29 Citations

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Abstract

 We consider a nearest neighbor walk on a regular tree, with transition probabilities proportional to weights or conductances of the edges. Initially all edges have weight 1, and the weight of an edge is increased to $c > 1$ when the edge is traversed for the first time. After such a change the weight of an edge stays at $c$ forever. We show that such a walk is transient for all values of $c \ge 1$, and that the walk moves off to infinity at a linear rate. We also prove an invariance principle for the height of the walk.

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Authors and Affiliations

  1. Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853, USA. e-mail: rtd1@cornell.edu; kesten@math.cornell.edu; limic@math.cornell.edu, , , , , , US

    Rick Durrett, Harry Kesten & Vlada Limic

Authors
  1. Rick Durrett
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  2. Harry Kesten
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  3. Vlada Limic
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Additional information

Received: 6 March 2001 / Revised version: 16 July 2001 / Published online: 15 March 2002

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Durrett, R., Kesten, H. & Limic, V. Once edge-reinforced random walk on a tree. Probab Theory Relat Fields 122, 567–592 (2002). https://doi.org/10.1007/s004400100179

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  • Issue Date: April 2002

  • DOI: https://doi.org/10.1007/s004400100179

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Keywords

  • Random Walk
  • Invariance Principle
  • Linear Rate
  • Regular Tree
  • Neighbor Walk
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