  We prove a law of large numbers for a class of multidimensional random walks
in random environments where the environment satisfies appropriate mixing
conditions, which hold when the environment is a weak mixing field in the sense
of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments
of some random times depending on the path. It applies in the non-nestling
case, but we also provide examples of nestling walks that satisfy our
assumptions. The derivation is based on an adaptation, using coupling, of the
regeneration argument of Sznitman-Zerner.
