Communications in Mathematical Physics

, Volume 85, Issue 3, pp 449–470 | Cite as

Symmetric random walks in random environments

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


We consider a random walk on thed-dimensional lattice ℤ d 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.


Neural Network Statistical Physic Probability Distribution Complex System Random Walk 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • V. V. Anshelevich
    • 1
  • K. M. Khanin
    • 2
  • Ya. G. Sinai
    • 2
  1. 1.Institute of Molecular GeneticsAcademy of Science of USSRMoscowUSSR
  2. 2.L. D. Landau Institute for Theoretical PhysicsAcademy of Science of USSRMoscowUSSR

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