Symmetric random walks in random environments

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.