We establish an abstract quenched linear response result for random dynamical
systems, which we then apply to the case of smooth expanding on average
cocycles on the unit circle. In sharp contrast to the existing results in the
literature, we deal with the class of random dynamics that does not necessarily
exhibit uniform decay of correlations. Our techniques rely on the
infinite-dimensional ergodic theory and in particular, on the study of the top
Oseledets space of a parametrized transfer operator cocycle.
