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May 2002 Asymptotic properties of certain anisotropic walks in random media
Lian Shen
Ann. Appl. Probab. 12(2): 477-510 (May 2002). DOI: 10.1214/aoap/1026915612


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.


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Lian Shen. "Asymptotic properties of certain anisotropic walks in random media." Ann. Appl. Probab. 12 (2) 477 - 510, May 2002.


Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1016.60092
MathSciNet: MR1910636
Digital Object Identifier: 10.1214/aoap/1026915612

Primary: 60K37 , 82D30

Keywords: asymptotic random walks , ballistic walks , Random media

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 2 • May 2002
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