Abstract: The central limit theorem (CLT) for (partially) expanding or hyperbolic dynamical systems was extensively studied in the past decades (including quantitative and local versions etc.)
A random dynamical system (RDS) is formed by compositions of random stationary maps along orbits of a "driving system" (MPS). Limit theorems for uniformly expanding RDS have been studied extensively in the past years. In the non-uniform case, some results with verifiable conditions exist only for independent maps.
 We present the first types of explicit  sufficient conditions for the CLT for randomnon-uniformly expanding dynamical systems, which are not driven by an iid sequence. Our approach
is based on proving an “effective” random Perron-Frobenius "rates" for the products of the underlying random transfer operators (which allows to bypass certain difficulties arising from Oseledets theorem), together with certain weak upper mixing type assumptions on the driving system.