# Relative Complexity of Random Walks in Random Scenery in the absence of a weak invariance principle for the local times

@article{Deligiannidis2015RelativeCO,
title={Relative Complexity of Random Walks in Random Scenery in the absence of a weak invariance principle for the local times},
author={George Deligiannidis and Zemer Kosloff},
journal={arXiv: Probability},
year={2015}
}
• Published 1 June 2015
• Mathematics
• arXiv: Probability
We answer the 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 F\"olner property almost surely.
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Mixing properties of the generalized T, T-1-process
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• 1996
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