# Sharp Statistical Properties for a Family of Multidimensional NonMarkovian Nonconformal Intermittent Maps

## TL;DR

This paper establishes sharp polynomial decay bounds and statistical limit laws for a class of multidimensional intermittent maps, extending known results from one-dimensional cases to higher dimensions despite nonconformality challenges.

## Contribution

It introduces methods to prove optimal decay rates and statistical limit laws for multidimensional nonconformal intermittent maps, a problem previously only partially addressed.

## Key findings

- Proves sharp polynomial bounds on decay of correlations.
- Extends statistical limit laws from 1D to multidimensional maps.
- Demonstrates convergence to stable laws and infinite measure mixing.

## Abstract

Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that up to now is only partially addressed. We show how to prove sharp polynomial bounds on decay of correlations for a class of multidimensional intermittent maps. In addition we show that the optimal results on statistical limit laws for one-dimensional intermittent maps hold also for the maps considered here. This includes the (functional) central limit theorem and local limit theorem, Berry-Esseen estimates, large deviation estimates, convergence to stable laws and L\'evy processes, and infinite measure mixing.