The need for speed: maximizing the speed of random walk in fixed environments
نویسندگان
چکیده
We study nearest neighbor random walks in fixed environments of Z composed of two point types : ( 1 2 , 1 2 ) and (p, 1− p) for p > 1 2 . We show that for every environment with density of p drifts bounded by λ we have lim supn→∞ Xn n ≤ (2p − 1)λ, where Xn is a random walk in the environment. In addition up to some integer effect the environment which gives the greatest speed is given by equally spaced drifts.
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