  The periodic Lorentz gas describes the dynamics of a point particle in a
periodic array of spherical scatterers, and is one of the fundamental models
for chaotic diffusion. In the present paper we investigate the Boltzmann-Grad
limit, where the radius of each scatterer tends to zero, and prove the
existence of a limiting distribution for the free path length of the periodic
Lorentz gas. We also discuss related problems, such as the statistical
distribution of directions of lattice points that are visible from a fixed
position.
