Quenched limit theorems for expanding on average cocycles

Abstract

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method for nonautonomous dynamics developed by [D. Dragičević, G. Froyland, C. Gonzàlez-Tokman and S. Vaienti, A spectral approach for quenched limit theorems for random expanding dynamical systems, Commun. Math. Phys. 360 (2018) 1121–1187], to deal with the case of random dynamics that exhibits nonuniform decay of correlations, which are ubiquitous in the context of the multiplicative ergodic theory.