Excited against the tide: A random walk with competing drifts

Abstract

We study a random walk that has a drift $\frac{\beta }{d}$ to the right when located at a previously unvisited vertex and a drift $\frac{\mu }{d}$ to the left otherwise. We prove that in high dimensions, for every $\mu$, the drift to the right is a strictly increasing and continuous function of $\beta$, and that there is precisely one value ${\beta }_0(\mu ,d)$ for which the resulting speed is zero.

10 pages

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