Concentration inequalities for random dynamical systems

Abstract

We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random quantities, including time-average synchronization, empirical measures, Birkhoff sums, and correlation dimension estimators. We present concrete classes of RDSs to which our main results apply, such as finitely supported diffeomorphisms on the circle and projective systems induced by linear cocycles. In both cases, we obtain concentration inequalities for finite-time Lyapunov exponents.