# Mixing rate in infinite measure for Z^d-extension, application to the periodic Sinai billiard

## TL;DR

This paper investigates the mixing rates of Z^d-extensions in dynamical systems, specifically applying the findings to the periodic Sinai billiard, and relates it to the local limit theorem.

## Contribution

It introduces a new approach to determine mixing rates in Z^d-extensions and applies it to the Z^2-periodic Sinai billiard, comparing it with existing induction methods.

## Key findings

- Established a rate of mixing for Z^2-periodic Sinai billiard.
- Linked mixing rates to the local limit theorem.
- Compared new approach with induction method.

## Abstract

We study the rate of mixing of observables of Z^d-extensions of probability preserving dynamical systems. We explain how this question is directly linked to the local limit theorem and establish a rate of mixing for general classes of observables of the Z^2-periodic Sinai billiard. We compare our approach with the induction method.