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

George Deligiannidis; Zemer Kosloff

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arXiv · 1506.00422

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

George Deligiannidis·Zemer Kosloff

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Abstract

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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BibTeX RIS

George Deligiannidis, Zemer Kosloff. 2015-06-01. Relative Complexity of Random Walks in Random Scenery in the absence of a weak invariance principle for the local times. https://arxiv.org/abs/1506.00422

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