Math @ Duke

Publications [#243497] of Richard T. Durrett
Papers Published
 Durrett, R; Kesten, H; Limic, V, Once edgereinforced random walk on a tree,
Probability Theory and Related Fields, vol. 122 no. 4
(2002),
pp. 567592 [doi]
(last updated on 2018/03/24)
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 ≥ 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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