Compound Poisson distributions for random dynamical systems

We show that quenched limiting hitting distributions are
compound Poisson distributed for certain random dynamical systems with
targets.
Targets are random and assumed to have well-defined return statistics
of certain type, which turn out to characterize the said compound
Poissonian limit.
Moreover, quenched and annealed polynomial decay of correlations are
assumed, whereas annealed Kac-time normalization is adopted.
Examples discussed are one-dimensional random piecewise expanding systems.
Based on joint work with N. Haydn and S. Vaienti.