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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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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DOI: https://doi.org/10.1007/s004400100179
Keywords
- Random Walk
- Invariance Principle
- Linear Rate
- Regular Tree
- Neighbor Walk