Once edge-reinforced random walk on a tree


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Kesten, H; Limic, V

Published Date

  • April 1, 2002

Published In

Volume / Issue

  • 122 / 4

Start / End Page

  • 567 - 592

International Standard Serial Number (ISSN)

  • 0178-8051

Digital Object Identifier (DOI)

  • 10.1007/s004400100179

Citation Source

  • Scopus