# Infinite measure mixing for some mechanical systems

## TL;DR

This paper demonstrates that certain infinite measure-preserving systems, well approximated by systems satisfying the local limit theorem, exhibit mixing behavior with respect to global observables, including models like the Lorentz gas and Fermi-Ulam pingpongs.

## Contribution

It establishes a link between local limit theorem approximations and mixing properties in infinite measure systems, covering several physical models.

## Key findings

- Systems satisfying the conditions include Lorentz gas with Coulomb potential
- Galton board and Fermi-Ulam pingpongs also satisfy the conditions
- Original systems exhibit mixing with respect to global observables

## Abstract

We show that if an infinite measure preserving system is well approximated on most of the phase space by a system satisfying the local limit theorem, then the original system enjoys mixing with respect to global observables, that is, the observables which admit an infinite volume average. The systems satisfying our conditions include the Lorentz gas with Coulomb potential, the Galton board and piecewise smooth Fermi-Ulam pingpongs.