# Functional correlation decay and multivariate normal approximation for non-uniformly expanding maps

## TL;DR

This paper establishes a functional correlation bound for intermittent Pomeau-Manneville maps with time-dependent parameters, enabling the derivation of multivariate central limit theorems with convergence rates for these non-uniformly expanding systems.

## Contribution

It introduces a new correlation bound applicable to non-autonomous Pomeau-Manneville maps, facilitating the use of Stein and Rio's normal approximation methods for these models.

## Key findings

- Derived a functional correlation bound for intermittent maps.
- Proved multivariate CLT with convergence rates for specific parameter ranges.
- Applied the bound to establish normal approximation results for non-uniformly expanding maps.

## Abstract

In the setting of intermittent Pomeau-Manneville maps with time dependent parameters, we show a functional correlation bound widely useful for the analysis of the statistical properties of the model. We give two applications of this result, by showing that in a suitable range of parameters the bound implies the conditions of the normal approximation methods of Stein and Rio. For a single Pomeau-Manneville map belonging to this parameter range, both methods then yield a multivariate central limit theorem with a rate of convergence.