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Probability Theory and Related Fields

, Volume 122, Issue 4, pp 567–592 | Cite as

Once edge-reinforced random walk on a tree

  • Rick Durrett
  • Harry Kesten
  • Vlada Limic

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.

Keywords

Random Walk Invariance Principle Linear Rate Regular Tree Neighbor Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Rick Durrett
    • 1
  • Harry Kesten
    • 1
  • Vlada Limic
    • 1
  1. 1.Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853, USA. e-mail: rtd1@cornell.edu; kesten@math.cornell.edu; limic@math.cornell.eduUS

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