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Symmetric random walks in random environments

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Abstract

We consider a random walk on thed-dimensional lattice ℤd where the transition probabilitiesp(x,y) are symmetric,p(x,y)=p(y,x), different from zero only ify−x belongs to a finite symmetric set including the origin and are random. We prove the convergence of the finite-dimensional probability distributions of normalized random paths to the finite-dimensional probability distributions of a Wiener process and find our an explicit expression for the diffusion matrix.

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Communicated by A. Jaffe

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Anshelevich, V.V., Khanin, K.M. & Sinai, Y.G. Symmetric random walks in random environments. Commun.Math. Phys. 85, 449–470 (1982). https://doi.org/10.1007/BF01208724

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  • DOI: https://doi.org/10.1007/BF01208724

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