On the limiting velocity of random walks in mixing random environment

We consider random walks in strong-mixing random Gibbsian environments in Z, d ≥ 2. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment [8]. Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions (d ≥ 5).