  Entropy dimension is an entropy-type quantity which takes values in $[0,1]$
and classifies different levels of intermediate growth rate of complexity for
dynamical systems. In this paper, we consider the complexity of skew products
of irrational rotations with Bernoulli systems, which can be viewed as
deterministic walks in random sceneries, and show that this class of models can
have any given entropy dimension by choosing suitable rotations for the base
system.

Dynamical Systems