Limit laws for random walk in a dynamic path-cone mixing random environment

We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. Assuming that the environment decorrelates with time by satisfying the “path-cone”-mixing property introduced in [8, Bethuelsen and Völlering], we prove a strong law of large numbers and large deviation estimates. Moreover, under a mild assumption on the decay rate of this mixing property, we obtain a functional central limit theorem under the annealed law.