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

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Abstract

We study nearest neighbor random walks in fixed environments of 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 λ we have lim sup n→∞ Xn/n ≤ (2p-1)λ, where X n is a random walk in the environment. In addition up to some integer effect the environment which gives the greatest speed is given by equally spaced drifts.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalElectronic Journal of Probability
Volume17
DOIs
StatePublished - Feb 2012

Keywords

  • Environment
  • Random walk
  • Speed

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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