Symmetric random walks in random environments

V. V. Anshelevich; K. M. Khanin; Ya G. Sinai

doi:10.1007/BF01208724

Symmetric random walks in random environments

V. V. Anshelevich, K. M. Khanin, Ya G. Sinai

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Abstract

We consider a random walk on the d-dimensional lattice ℤ^d where the transition probabilities p(x,y) are symmetric, p(x,y)=p(y,x), different from zero only if y-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.

Original language	English (US)
Pages (from-to)	449-470
Number of pages	22
Journal	Communications In Mathematical Physics
Volume	85
Issue number	3
DOIs	https://doi.org/10.1007/BF01208724
State	Published - Sep 1982

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01208724

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year = "1982",

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N2 - We consider a random walk on the d-dimensional lattice ℤd where the transition probabilities p(x,y) are symmetric, p(x,y)=p(y,x), different from zero only if y-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.

AB - We consider a random walk on the d-dimensional lattice ℤd where the transition probabilities p(x,y) are symmetric, p(x,y)=p(y,x), different from zero only if y-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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Symmetric random walks in random environments

Abstract

All Science Journal Classification (ASJC) codes

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