Limit theorems for some skew products with mixing base maps

We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om x)$togetherwitha$T$-invariantmeasure,whosebasemap$\te$ satisfies certain topological and mixing conditions and the maps $T_{\text{om}}$ on the fibers are certain non-singular distance expanding maps. Our results hold true when $\text{te}$ is either a sufficiently fast mixing Markov shift or a (non-uniform) Young tower with at least one periodic point and polynomial tails. %In fact, our conditions will be satisfied %when $\text{om}$ is the whole orbit the towers. The proofs are based on the random complex Ruelle-Perron-Frobenius theorem from \cite{book} applied with appropriate random transfer operators generated by $T_{\text{om}}$, together with certain regularity assumptions (as functions of $\text{om}$) of these operators. Limit theorems for deterministic processes whose distributions on the fibers are generated by Markov chains with transition operators satisfying a random version of the Doeblin condition will also be obtained. The main innovation in this paper is that the results hold true even though the spectral theory used in \cite{Aimino} does not seem to be applicable, and the dual of the Koopman operator of $T$ (with respect to the invariant measure) does not seem to have a spectral gap.