## Electronic Communications in Probability

### Excited Random Walk

#### Abstract

A random walk on $\mathbb{Z}^d$ is excited if the first time it visits a vertex there is a bias in one direction, but on subsequent visits to that vertex the walker picks a neighbor uniformly at random. We show that excited random walk on $\mathbb{Z}^d$ is transient iff $d \gt 1$.

#### Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 9, 86-92.

Dates
Accepted: 24 June 2003
First available in Project Euclid: 18 May 2016

https://projecteuclid.org/euclid.ecp/1463608893

Digital Object Identifier
doi:10.1214/ECP.v8-1072

Mathematical Reviews number (MathSciNet)
MR1987097

Zentralblatt MATH identifier
1060.60043

Keywords
Perturbed random walk transience

Rights

#### Citation

Benjamini, Itai; Wilson, David. Excited Random Walk. Electron. Commun. Probab. 8 (2003), paper no. 9, 86--92. doi:10.1214/ECP.v8-1072. https://projecteuclid.org/euclid.ecp/1463608893

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