The Annals of Applied Probability

Asymptotic properties of certain anisotropic walks in random media

Lian Shen

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Abstract

We discuss a class of anisotropic random walks in a random media on$\mathbb{Z}^{d}$, $d\geq1$, which have reversible transition kernels when the environment is fixed. The aim is to derive a strong law of large numbers and a functional central limit theorem for this class of models. The technique of the environment viewed from the particle does not seem to apply well in this setting. Our approach is based on the technique of introducing certain times similar to the regeneration times in the work concerning random walks in i.i.d. random environment by Sznitman and Zerner. With the help of these times we are able to construct anergodic Markov structure.

Article information

Source
Ann. Appl. Probab., Volume 12, Number 2 (2002), 477-510.

Dates
First available in Project Euclid: 17 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1026915612

Digital Object Identifier
doi:10.1214/aoap/1026915612

Mathematical Reviews number (MathSciNet)
MR1910636

Zentralblatt MATH identifier
1016.60092

Subjects
Primary: 60K37: Processes in random environments 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Random media ballistic walks asymptotic random walks

Citation

Shen, Lian. Asymptotic properties of certain anisotropic walks in random media. Ann. Appl. Probab. 12 (2002), no. 2, 477--510. doi:10.1214/aoap/1026915612. https://projecteuclid.org/euclid.aoap/1026915612


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