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}
}
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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