  We study random circle maps that are expanding on the average. Uniform bounds
on neither expansion nor distortion are required. We construct a coupling
scheme, which leads to exponential convergence of measures (memory loss) and
exponential mixing. Leveraging from the structure of the associated correlation
estimates, we prove an almost sure invariance principle for vector-valued
observables. The motivation for our paper is to explore these methods in a
nonuniform random setting.
