## The Annals of Probability

### 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 Fölner property almost surely.

#### Article information

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

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

https://projecteuclid.org/euclid.aop/1502438433

Digital Object Identifier
doi:10.1214/16-AOP1118

Mathematical Reviews number (MathSciNet)
MR3693968

Zentralblatt MATH identifier
1380.37011

#### Citation

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. https://projecteuclid.org/euclid.aop/1502438433

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