Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system

TL;DR

This paper proves that certain nonuniformly hyperbolic random maps exhibit exponential decay of correlations in a quenched setting, using cone techniques and transfer operators, with applications to Lorenz maps and Axiom A attractors.

Contribution

It introduces a method to establish quenched exponential correlation decay for random tower maps with exponential tails, extending to non-iid systems.

Findings

Proves quenched exponential decay of correlations for random tower maps.

Applies results to small random perturbations of Lorenz maps.

Demonstrates decay in systems with non-iid randomness.

Abstract

In this article we study random tower maps driven by an ergodic automorphism. We prove quenched exponential correlations decay for tower maps admitting exponential tails. Our technique is based on constructing suitable cones of functions, defined on the random towers, which contract with respect to the Hilbert metric under the action of appropriate transfer operators. We apply our results to obtain quenched exponential correlations decay for several non-iid random dynamical systems including small random perturbations of Lorenz maps and Axiom A attractors.