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

  
@article{EJP1800,
	author = {Eviatar Procaccia and Ron Rosenthal},
	title = {The need for speed: maximizing the speed of random walk in fixed environments},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Random walk ; Speed ; Environment},
	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.},
	pages = {no. 13, 1-19},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1800},    
        url = {http://ejp.ejpecp.org/article/view/1800}}