Quenched limit theorems for expanding on average cocycles

TL;DR

This paper establishes quenched limit theorems, including CLT and large deviations, for expanding on average cocycles using a modified spectral method suited for nonuniform decay in random dynamics.

Contribution

It introduces a novel spectral method adaptation to prove quenched limit theorems for non-autonomous, nonuniformly mixing dynamical systems, answering a question by Buzzi.

Findings

Proved quenched central limit theorem for expanding on average cocycles.

Established large deviations principle in the quenched setting.

Derived local central limit theorem for the studied 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 non-autonomous dynamics developed by Dragi\v{c}evi\'{c} et al., 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. Our results provide an affirmative answer to a question posed by Buzzi.