The Statistics of the large-scale Velocity Field

A lot of predictions for the statistical properties of the cosmic velocity field at large-scale have been obtained recently using perturbation theory. In this contribution I report the outcomes of a set of numerical tests that aim to check these results. Using Voronoi and Delaunay tessellations for defining the velocity field by interpolation between the particle velocities in numerical simulations, we have been able to get reliable estimates of the local velocity gradients. Thus, we have been able to show that the properties of the velocity divergence are in very good agreement with the analytical results. In particular we have confirmed the $\mathrm{\Omega }$ dependence expected for the shape of its distribution function.