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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:
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 Folner property almost surely.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1214/16-AOP1118

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Annals of Probability Journal website
Volume:
45
Issue:
4
Pages:
2505-2532
Publication date:
2017-08-01
Acceptance date:
2016-04-23
DOI:
ISSN:
0091-1798
Source identifiers:
526082
Keywords:
Pubs id:
pubs:526082
UUID:
uuid:aab71c02-0bfe-4c74-80c2-8cf020376911
Local pid:
pubs:526082
Deposit date:
2016-05-02

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