Statistical properties of Lorentz gases on aperiodic tilings, Part 1

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.