Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

George Deligiannidis; Zemer Kosloff

doi:10.1214/16-AOP1118

Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

George Deligiannidis
, Zemer Kosloff

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2505-2532
Number of pages	28
Journal	Annals of Probability
Volume	45
Issue number	4
DOIs	https://doi.org/10.1214/16-AOP1118
State	Published - 1 Jul 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2017.

Keywords

Entropy
Fölner sequence
Random walk in random scenery
Relative complexity

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10.1214/16-AOP1118

Cite this

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Relative complexity of Random walks in Random scenery in the absence of a weak invariance principle for the local times

Abstract

Bibliographical note

Keywords

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