Random walk in random environment and mixing

Sammanfattning: A random walk in a random environment is obtained by first choosing an environment according to some probability measure (the random environment).Once the environment is chosen, a random walk is performed in that particularenvironment.In Solomon (1975) criteria for recurrence were given and, in the transientcase, Kesten, Kozlov and Spitzer (1975) proved normal convergence for an i.i.d.environment. Our main results are extensions to weak invariance principles andlaws of the iterated logarithm for i.i.d. environments, as well as for stationaryenvironments satisfying some mixing conditions, and for independent, non-i.i.d.environments.