## The Annals of Probability

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

### 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

#### 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**

Received: May 2015

Revised: December 2015

First available in Project Euclid: 11 August 2017

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/16-AOP1118

**Mathematical Reviews number (MathSciNet)**

MR3693968

**Zentralblatt MATH identifier**

1380.37011

**Subjects**

Primary: 37A35: Entropy and other invariants, isomorphism, classification 60F05: Central limit and other weak theorems

Secondary: 37A05: Measure-preserving transformations

**Keywords**

Random walk in random scenery relative complexity entropy Fölner sequence

#### 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