  We calculate the diffusion coefficients of persistent random walks on cubic
and hypercubic lattices, where the direction of a walker at a given step
depends on the memory of one or two previous steps. These results are then
applied to study a billiard model, namely a three-dimensional periodic Lorentz
gas. The geometry of the model is studied in order to find the regimes in which
it exhibits normal diffusion. In this regime, we calculate numerically the
transition probabilities between cells to compare the persistent random-walk
approximation with simulation results for the diffusion coefficient.
