Central limit theorem for a random walk in dynamical environment: integral and local.

In the paper a model of a random walk on the d-dimensional lattice Z^d, d = 1, 2, . . . , in a dynamic environment which is i.i.d. in space-time is considered. The environment is described by a field which locally takes values in a finite set. We prove that: - If the stochastic term is small the central limit theorem holds almost surely, with the same parameters as for the random walk with averaged transition probabilities (averaged RW). - The leading term in the asymptotics for large t differs from the corresponding term for the averaged walk by a factor depending on the field “as seen from the final point”.