## The Annals of Probability

### Relative complexity of random walks in random sceneries

Jon Aaronson

#### Abstract

Relative complexity measures the complexity of a probability preserving transformation relative to a factor being a sequence of random variables whose exponential growth rate is the relative entropy of the extension. We prove distributional limit theorems for the relative complexity of certain zero entropy extensions: RWRSs whose associated random walks satisfy the $\alpha$-stable CLT ($1<\alpha\le2$). The results give invariants for relative isomorphism of these.

#### Article information

Source
Ann. Probab., Volume 40, Number 6 (2012), 2460-2482.

Dates
First available in Project Euclid: 26 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.aop/1351258732

Digital Object Identifier
doi:10.1214/11-AOP688

Mathematical Reviews number (MathSciNet)
MR3050509

Zentralblatt MATH identifier
1258.37004

#### Citation

Aaronson, Jon. Relative complexity of random walks in random sceneries. Ann. Probab. 40 (2012), no. 6, 2460--2482. doi:10.1214/11-AOP688. https://projecteuclid.org/euclid.aop/1351258732

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