  The Lyapunov spectra of random U(1) extensions of expanding maps on the torus
were investigated in our previous work [NW2015]. Using the result, we extend
the recent spectral approach for quenched limit theorems for expanding maps
[DFGV2018] and hyperbolic maps [DFGV2019] to our partially hyperbolic dynamics.
Quenched central limit theorems, large deviations principles and local central
limit theorems for random U(1) extensions of expanding maps on the torus are
proved via corresponding theorems for abstract random dynamical systems.
