The Annals of Probability

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

George Deligiannidis and Zemer Kosloff

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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.

Article information

Ann. Probab., Volume 45, Number 4 (2017), 2505-2532.

Received: May 2015
Revised: December 2015
First available in Project Euclid: 11 August 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37A35: Entropy and other invariants, isomorphism, classification 60F05: Central limit and other weak theorems
Secondary: 37A05: Measure-preserving transformations

Random walk in random scenery relative complexity entropy Fölner sequence


Deligiannidis, George; Kosloff, Zemer. Relative complexity of random walks in random scenery in the absence of a weak invariance principle for the local times. Ann. Probab. 45 (2017), no. 4, 2505--2532. doi:10.1214/16-AOP1118.

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