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2012 The need for speed: maximizing the speed of random walk in fixed environments
Eviatar Procaccia, Ron Rosenthal
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Electron. J. Probab. 17: 1-19 (2012). DOI: 10.1214/EJP.v17-1800

Abstract

We study nearest neighbor random walks in fixed environments of $\mathbb{Z}$ composed of two point types : $(\frac{1}{2},\frac{1}{2})$ and$(p,1-p)$ for $p>\frac{1}{2}$. We show that for every environmentwith density of $p$ drifts bounded by $\lambda$ we have $\limsup_{n\rightarrow\infty}\frac{X_n}{n}\leq (2p-1)\lambda$, where $X_n$ is a random walk in the environment. In addition up to some integereffect the environment which gives the greatest speed is given byequally spaced drifts.

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Eviatar Procaccia. Ron Rosenthal. "The need for speed: maximizing the speed of random walk in fixed environments." Electron. J. Probab. 17 1 - 19, 2012. https://doi.org/10.1214/EJP.v17-1800

Information

Accepted: 11 February 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1248.60049
MathSciNet: MR2892326
Digital Object Identifier: 10.1214/EJP.v17-1800

Subjects:
Primary: 60-XX

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