Equally spaced drifts maximize the speed of one-dimensional random walks

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Consider random walks in environments on Z{\mathbb{Z}} composed of two types, (p,1−p)(p,1-p) and (q,1−q)(q,1-q), where 12<p<q<1\frac{1}{2}<p<q<1. Equally spaced drifts conjecture. An environment which maximizes the speed is given, up to some integer effect, by equally spaced drifts. The conjecture proposes the speed-maximizing arrangement for these two-point environments; the source does not state a resolution, so its status remains open.

References

Primary source

Eviatar B. Procaccia and Ron Rosenthal, “The need for speed : Maximizing random walks speed on fixed environments”, arXiv:1109.0832 (2012).

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