Relative complexity of random walks in random sceneries

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 a- stable CLT (1< α ≤ 2). The results give invariants for relative isomorphism of these.