Diffusion for the periodic wind-tree model

TL;DR

This paper proves that in a periodic wind-tree billiard model, the diffusion rate is generically 2/3 regardless of scatterer size, revealing a universal diffusive behavior in this infinite billiard system.

Contribution

It establishes the polynomial diffusion rate of 2/3 for the periodic wind-tree model, independent of scatterer size, for generic angles.

Findings

Diffusion rate is 2/3 for generic angles

Diffusion behavior is universal across scatterer sizes

Provides rigorous proof for diffusion rate in infinite billiards

Abstract

The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers disposed at each integer point. We prove that independently of the size of the scatterers, generically with respect to the angle, the polynomial diffusion rate in this billiard is 2/3.