Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates

TL;DR

This paper establishes explicit conditions under which the central limit theorem and related probabilistic results hold for non-uniformly partially expanding random dynamical systems with random Gibbs measures.

Contribution

It provides the first explicit sufficient conditions for CLT and related results in non-uniformly expanding random dynamical systems with random Gibbs measures.

Findings

Proves CLT, invariance principle, and deviations for non-uniformly expanding systems.

Derives Berry-Esseen estimates and local CLT under specified conditions.

Establishes a framework for analyzing stochastic processes in complex dynamical systems.

Abstract

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as stochastic processes together with some random Gibbs measure. More precisely, we prove a central limit theorem (CLT), an almost sure invariance principle, a moderate deviations principle, Berry-Esseen type estimates and a moderate local central limit theorem for random Birkhoff sums generated by a non-uniformly partially expanding dynamical systems $T_\omega$ and a random Gibbs measure $\mu_\omega$ corresponding to a random potential $\phi_\omega$ with a sufficiently regular variation.