Distribution of the linear flow length in a honeycomb in the small-scatterer limit

We study the statistics of the linear flow in a punctured honeycomb lattice, or equivalently the free motion of a particle on a regular hexagonal billiard table with holes of equal size at the corners and obeying the customary reflection rules. In the small-scatterer limit we prove the existence of the limiting distribution of the free path length with randomly chosen origin of the trajectory and explicitly compute it.