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Excited random walk. (English) Zbl 1060.60043
Summary: 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 $$d>1$$.

##### MSC:
 60G50 Sums of independent random variables; random walks 60K37 Processes in random environments
##### Keywords:
perturbed random walk; transience
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