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.
"Relative complexity of random walks in random sceneries." Ann. Probab. 40 (6) 2460 - 2482, November 2012. https://doi.org/10.1214/11-AOP688