  Consider a point particle moving through a Poisson distributed array of cubes
all oriented along the axes - the random wind-tree model introduced in
Ehrenfest-Ehrenfest (1912). We show that, in the joint Boltzmann-Grad and
diffusive limit this process satisfies an invariance principle. That is, the
process converges in distribution to a Brownian motion in a particular scaling
limit. In a previous paper (2019) the authors used a novel coupling method to
prove the same statement for the random Lorentz gas with spherical scatterers.
In this paper we show that, despite the change in dynamics, the same strategy
with some modification can be used to prove an invariance principle for the
random wind-tree model.
