Quenched decay of correlations for one dimensional random Lorenz maps

TL;DR

This paper investigates how small random perturbations affect the mixing rates of one-dimensional Lorenz maps, demonstrating exponential decay of correlations for Holder observables using a random tower approach.

Contribution

It introduces a novel random tower construction to establish exponential quenched correlation decay in perturbed Lorenz maps.

Findings

Exponential decay of correlations for Holder observables.

Effective random tower construction for Lorenz maps.

Quantitative rates of mixing under small random perturbations.

Abstract

We study rates of mixing for small random perturbations of one dimensional Lorenz maps. Using a random tower construction, we prove that, for Holder observables, the random system admits exponential rates of quenched correlation decay.