Open Access
November 2012 Relative complexity of random walks in random sceneries
Jon Aaronson
Ann. Probab. 40(6): 2460-2482 (November 2012). DOI: 10.1214/11-AOP688


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.


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Jon Aaronson. "Relative complexity of random walks in random sceneries." Ann. Probab. 40 (6) 2460 - 2482, November 2012.


Published: November 2012
First available in Project Euclid: 26 October 2012

zbMATH: 1258.37004
MathSciNet: MR3050509
Digital Object Identifier: 10.1214/11-AOP688

Primary: 37A35 , 60F05
Secondary: 37A05 , 37A50 , 60F17

Keywords: $[T,T^{-1}]$ transformation , entropy dimension , Local time , Random walk in random scenery , Relative complexity , Symmetric stable process

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 6 • November 2012
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