Exact generating function for the two-dimensional lattice Lorentz gas

We find the generating function for the two-dimensional lattice Lorentz gas by the resolvent matrix method introducing a direct procedure to calculate its elements. The asymptotic behaviour of properties as moments of the distribution and the probability of returning to the origin is analyzed in the discrete time formulation, and extended to continuous time; we also discuss briefly a disordered model. This result can be applied to a variety of physical problems.