## Once edge-reinforced random walk on a tree

Publication
, Journal Article

Durrett, R; Kesten, H; Limic, V

Published in: Probability Theory and Related Fields

April 1, 2002

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.

### Duke Scholars

## Published In

Probability Theory and Related Fields

## DOI

## ISSN

0178-8051

## Publication Date

April 1, 2002

## Volume

122

## Issue

4

## Start / End Page

567 / 592

## Related Subject Headings

- Statistics & Probability
- 0104 Statistics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Durrett, R., Kesten, H., & Limic, V. (2002). Once edge-reinforced random walk on a tree.

*Probability Theory and Related Fields*,*122*(4), 567–592. https://doi.org/10.1007/s004400100179Durrett, R., H. Kesten, and V. Limic. “Once edge-reinforced random walk on a tree.”

*Probability Theory and Related Fields*122, no. 4 (April 1, 2002): 567–92. https://doi.org/10.1007/s004400100179.Durrett R, Kesten H, Limic V. Once edge-reinforced random walk on a tree. Probability Theory and Related Fields. 2002 Apr 1;122(4):567–92.

Durrett, R., et al. “Once edge-reinforced random walk on a tree.”

*Probability Theory and Related Fields*, vol. 122, no. 4, Apr. 2002, pp. 567–92.*Scopus*, doi:10.1007/s004400100179.Durrett R, Kesten H, Limic V. Once edge-reinforced random walk on a tree. Probability Theory and Related Fields. 2002 Apr 1;122(4):567–592.

## Published In

Probability Theory and Related Fields

## DOI

## ISSN

0178-8051

## Publication Date

April 1, 2002

## Volume

122

## Issue

4

## Start / End Page

567 / 592

## Related Subject Headings

- Statistics & Probability
- 0104 Statistics
- 0102 Applied Mathematics
- 0101 Pure Mathematics