Statistical properties of Lorentz gases on aperiodic tilings, Part 1

TL;DR

This paper investigates the statistical behavior of Lorentz gases on aperiodic tilings, demonstrating mixing and ergodicity properties using advanced dynamical systems techniques.

Contribution

It establishes the K property for the compact factor of the collision map and derives mixing and ergodicity results for Lorentz gases on aperiodic tilings.

Findings

The collision map's compact factor has the K property.

Lorentz gas flow exhibits planar ergodicity.

Pattern-equivariant functions are mixing.

Abstract

We consider the Lorentz gas model of category A (that is, with no corners and of finite horizon) on aperiodic repetitive tilings of $\mathbb{R}^2$ of finite local complexity. We show that the compact factor of the collision map has the K property, from which we derive mixing for pattern-equivariant functions as well as the planar ergodicity of the Lorentz gas flow.