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2013 On maximizing the speed of a random walk in fixed environments
Amichai Lampert, Assaf Shapira
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Electron. Commun. Probab. 18: 1-9 (2013). DOI: 10.1214/ECP.v18-2431

Abstract

We consider a random walk in a fixed $\mathbb{Z}$ environment composed of two point types: $q$-drifts (in which the probabiliy to move to the right is $q$, and $1-q$ to the left) and $p$-drifts, where $\frac{1}{2}<q<p$. We study the expected hitting time of a random walk at $N$ given the number of $p$-drifts in the interval $[1,N-1]$, and find that this time is minimized asymptotically by equally spaced $p$-drifts.

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Amichai Lampert. Assaf Shapira. "On maximizing the speed of a random walk in fixed environments." Electron. Commun. Probab. 18 1 - 9, 2013. https://doi.org/10.1214/ECP.v18-2431

Information

Accepted: 30 May 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1319.60092
MathSciNet: MR3070906
Digital Object Identifier: 10.1214/ECP.v18-2431

Subjects:
Primary: 60G50

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