Quenched decay of correlations for random contracting Lorenz maps

TL;DR

This paper proves that for certain randomly perturbed contracting Lorenz maps near a Rovella parameter, correlations decay exponentially, indicating rapid loss of memory in the system.

Contribution

It establishes exponential decay of quenched correlations for i.i.d. random perturbations of contracting Lorenz maps close to Rovella parameters, a novel result in the field.

Findings

Exponential decay of quenched correlations proven.

Applicable to maps near Rovella parameters.

Advances understanding of stochastic stability in chaotic systems.

Abstract

In this work, we consider i.i.d. random perturbations of contracting Lorenz maps sufficiently close to a Rovella parameter. We prove that the quenched correlations of the random dynamical system decay exponentially.