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The need for speed: maximizing the speed of random walk in fixed environments


 
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1. Title Title of document The need for speed: maximizing the speed of random walk in fixed environments
 
2. Creator Author's name, affiliation, country Eviatar Ben Procaccia; Weizmann Institute of Science; Israel
 
2. Creator Author's name, affiliation, country Ron Rosenthal; The Hebrew University of Jerusalem; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk ; Speed ; Environment
 
3. Subject Subject classification Probability theory and stochastic process
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-02-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1800
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1800
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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