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The purpose of this paper is to provide a first class of explicit sufficientconditions for the central limit theorem and related results in the setup ofnon-uniformly (partially) expanding non iid random transformations, consideredas stochastic processes together with some random Gibbs measure. Moreprecisely, we prove a central limit theorem (CLT), an almost sure invarianceprinciple, a moderate deviations principle, Berry-Esseen type estimates and amoderate local central limit theorem for random Birkhoff sums generated by anon-uniformly partially expanding dynamical systems $T_\omega$ and a randomGibbs measure $\mu_\omega$ corresponding to a random potential $\phi_\omega$with a sufficiently regular variation.

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