A Comparison of Random Walks in Dependent Random Environments

We provide exact computations for the drift of random walks in depen-dent random environments, including k-dependent and moving average envi-ronments. We show how the drift can be characterized and evaluated using Perron-Frobenius theory. Comparing random walks in various dependent en-vironments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random envi-ronment