Symmetric random walks in random environments
Abstract
We consider a random walk on the ddimensional lattice &Z;^{ d } where the transition probabilities p( x,y) are symmetric, p( x,y)= p( y,x), different from zero only if yx belongs to a finite symmetric set including the origin and are random. We prove the convergence of the finitedimensional probability distributions of normalized random paths to the finitedimensional probability distributions of a Wiener process and find our an explicit expression for the diffusion matrix.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 September 1982
 DOI:
 10.1007/BF01208724
 Bibcode:
 1982CMaPh..85..449A