Electronic Communications in Probability

Excited Random Walk

Itai Benjamini and David Wilson

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Perturbed random walk transience

This work is licensed under a Creative Commons Attribution 3.0 License.


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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