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 $d \gt 1$.
Citation
Itai Benjamini. David Wilson. "Excited Random Walk." Electron. Commun. Probab. 8 86 - 92, 2003. https://doi.org/10.1214/ECP.v8-1072
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