# Excited Random Walk

@article{Benjamini2003ExcitedRW,
title={Excited Random Walk},
author={Itai Benjamini and David Bruce Wilson},
journal={Electronic Communications in Probability},
year={2003},
volume={8},
pages={86-92}
}
• Published 22 February 2003
• Mathematics
• Electronic Communications in Probability
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 $d > 1$.
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