We give the results of a numerical study of the motion of a point particle in a d-
dimensional array of spherical scatterers (Sinai's billiard without horizon). We
find a simple universal law for the Lyapounov exponent (as a function of d) and
a stretched exponential decay for the velocity autocorrelation as a function of
the number of collisions. The diffusion seems to be anomalous in this problem.
Ergodicity is used to predict the shape of the probability distribution of long
free paths. Physical interpretations or clues are proposed.