The need for speed : Maximizing random walks speed on fixed environments

Abstract

We study nearest neighbor random walks on fixed environments of $\mathbb{Z}$ 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 $\lambda$ we have ${\mathrm{limsup}}_{n\to \infty }\frac{X_n}{n}\le (2p-1)\lambda$, 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.

References in corpus (2)

• Logarithmic speeds for one-dimensional perturbed random walk in random environment
• Mutually excited random walks

Cited by in corpus (2)

• Mutually excited random walks
• On Maximizing the Speed of a Random Walk in Fixed Environments