Once edge-reinforced random walk on a tree |
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Authors: | Rick Durrett Harry Kesten Vlada Limic |
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Affiliation: | (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 |
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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. Received: 6 March 2001 / Revised version: 16 July 2001 / Published online: 15 March 2002 |
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