# Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas

## TL;DR

This paper integrates martingale approximation techniques with anisotropic Banach spaces to establish statistical limit laws for the time-one map of a Lorentz gas, advancing understanding of dynamical systems' statistical properties.

## Contribution

It introduces a novel framework combining martingale approximations with anisotropic Banach spaces for analyzing Lorentz gas dynamics.

## Key findings

- Holder observables satisfy the central limit theorem
- Invariance principles are established for the system
- Framework can be applied to other dynamical systems

## Abstract

In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Holder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles.