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

DOI10.1214/EJP.V17-1800zbMATH Open1248.60049arXiv1109.0832MaRDI QIDQ428616

Publication date: 22 June 2012

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Abstract: We study nearest neighbor random walks on fixed environments of

m a t h b b 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

l a m b d a

we have

l i m s u p_{n i g h t a r r o w i n f t y} f r a c X_{n} n l e q (2 p - 1) l a m b d a

, where

X_{n}

is a random walk on the environment. In addition up to some integer effect the environment which gives the best speed is given by equally spaced drifts.

Full work available at URL: https://arxiv.org/abs/1109.0832

zbMATH Keywords

random walk environment speed

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Processes in random environments (60K37)