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arXiv · 2303.06756

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

Stein Andreas Bethuelsen·Florian Völlering
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Abstract

We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a strong law of large numbers and large deviation estimates assuming that the dynamic environment is "path-cone"-mixing. Under a mild assumption on the decay rate of this mixing property we further obtain a functional central limit theorem under the annealed law. Our method of proofs rest on the study of the so-called local environment process and general results for $\phi$-mixing stochastic processes.

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Stein Andreas Bethuelsen, Florian Völlering. 2023-03-12. Limit laws for random walks in a dynamic path-cone mixing random environment. https://arxiv.org/abs/2303.06756

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