Excited Random Walk

By Itai Benjamini, David Bruce Wilson. 2003

132 citations recorded by the source corpus.

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 $d > 1$.

Subfields: Mathematical Physics, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6cd0069c9e8cb8d908d1c773f9c2ba0cb545ea2b

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Citations in the corpus

Positively and negatively excited random walks on integers, with branching processes (2008, methodology): “Multi-dimensional ERW with cookies that induce a bias with a nonnegative projection in some fixed direction were considered in[ BW03 ],[Ko03],[Ko05],[Zer06], [HH06] and[BR07].”
On a general many-dimensional excited random walk (2010, methodology): “As explained in [4], it can be shown using the ideas of [3] that for every ε the number of tan points visited by (Ym) at time n is larger than n 3/4−ε with a probability that decays faster than any polynomial in n.”
A survey of random processes with reinforcement (2006, result): “ the ratio of the reinforcement parameter to the initial edge weights is less than 4/3. A slight variation on the deﬁnition of once-reinforced random walk gives the excited random walk, introduced in [BW03] and taken up in [Vol03; Zer06]. These results are too recent to have been included in this su”
Recurrence and transience for the frog model on trees (2014, background): “Another related process is excited random walk [4].”
On the speed of a cookie random walk (2006, unknown): “We consider the model of the multi-excited random walk, also called cookie random walk, introduced by Zerner in [10] as a generalization of the model of the excited random walk described by Benjamini and Wilson in [2] (see also Davis [3] for a continuous time analogue).”