Article

Probability Theory and Related Fields

, Volume 139, Issue 1, pp 41-64

Simple transient random walks in one-dimensional random environment: the central limit theorem

  • Ilya Ya. GoldsheidAffiliated withSchool of Mathematical Sciences, Queen Mary, University of London Email author 

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Abstract

We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the central limit theorem (CLT) holds for the position of the walk. Verifying these conditions leads to a complete solution of the problem in the case of independent identically distributed environments as well as in the case of uniformly ergodic (and thus also weakly mixing) environments.

Keywords

RWRE Simple random walks Quenched random environments Central limit theorem

Mathematics Subject Classification (2000)

Primary 60K37 Primary 60F05 Secondary 60J05 Secondary 82C44