Regularity of the variance in quenched CLT for random intermittent dynamical systems

TL;DR

This paper proves a quenched CLT for random LSV maps without mixing assumptions, showing the variance's regularity under perturbations, based on recent stability and linear response results.

Contribution

It establishes a quenched CLT for random intermittent maps and analyzes the regularity of the variance with respect to perturbations, extending previous stability results.

Findings

Quenched CLT holds for the studied random maps.

Variance varies continuously and differentiably under perturbations.

Results rely on recent advances in statistical stability and linear response.

Abstract

We study random dynamical systems composed of LSV maps with varying parameters, without any mixing assumptions on the base space of random dynamics. We establish a quenched central limit theorem and identify conditions under which the associated limit variance varies continuously and differentiably with respect to perturbations of the random dynamics. Our arguments rely on recent results on statistical stability and linear response for random intermittent maps established in Dragicevic et al. (J. Lond. Math. Soc. 111 (2025), e70150).