We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Fölner property almost surely.
Bibliographical notePublisher Copyright:
© Institute of Mathematical Statistics, 2017.
- Fölner sequence
- Random walk in random scenery
- Relative complexity