### 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) |
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Pages (from-to) | 449-470 |

Number of pages | 22 |

Journal | Communications In Mathematical Physics |

Volume | 85 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1982 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Anshelevich, V. V., Khanin, K. M., & Sinai, Y. G. (1982). Symmetric random walks in random environments.

*Communications In Mathematical Physics*,*85*(3), 449-470. https://doi.org/10.1007/BF01208724