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July 2017 Relative complexity of random walks in random scenery in the absence of a weak invariance principle for the local times
George Deligiannidis, Zemer Kosloff
Ann. Probab. 45(4): 2505-2532 (July 2017). DOI: 10.1214/16-AOP1118

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.

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George Deligiannidis. Zemer Kosloff. "Relative complexity of random walks in random scenery in the absence of a weak invariance principle for the local times." Ann. Probab. 45 (4) 2505 - 2532, July 2017. https://doi.org/10.1214/16-AOP1118

Information

Received: 1 May 2015; Revised: 1 December 2015; Published: July 2017
First available in Project Euclid: 11 August 2017

zbMATH: 1380.37011
MathSciNet: MR3693968
Digital Object Identifier: 10.1214/16-AOP1118

Subjects:
Primary: 37A35, 60F05
Secondary: 37A05

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 4 • July 2017
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