We present molecular dynamics simulations of the beginning of a silo
discharge by gravity. The evolution of the velocity profile and the probability
density functions for the displacements of the grains are obtained. These PDFs
reveal non-gaussian statistics and superdiffusive behavior similar to that observed
in some experiments. We propose an analytical expression for the PDFs and an
explanation for its dynamical origin in connection with the ideas of the “spot”
model and non-extensive thermodynamics.