The Annals of Probability

Relative complexity of random walks in random sceneries

Jon Aaronson

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

First available in Project Euclid: 26 October 2012

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Primary: 37A35: Entropy and other invariants, isomorphism, classification 60F05: Central limit and other weak theorems
Secondary: 37A05: Measure-preserving transformations 60F17: Functional limit theorems; invariance principles 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]

Relative complexity entropy dimension random walk in random scenery $[T,T^{-1}]$ transformation symmetric stable process local time


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

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