Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as stochastic processes together with some random Gibbs measure. More precisely, we prove a central limit theorem (CLT), an almost sure invariance principle, a moderate deviations principle, Berry-Esseen type estimates and a moderate local central limit theorem for random Birkhoff sums generated by a non-uniformly partially expanding dynamical systems $T_{\omega }$ and a random Gibbs measure ${\mu }_{\omega }$ corresponding to a random potential ${\phi }_{\omega }$ with a sufficiently regular variation.