Comparison of the one-point and smoothed PDFs estimated from the COVMOS and DEMNUni_cov experiments. Top: estimated one-point (solid lines) and smoothed (dashed lines) velocity PDF from one COVMOS simulation in red and one DEMNUni_cov simulation in black. The smoothed velocity PDF is estimated from a Delaunay tesselation of the particle coordinates of the DEMNUni_cov_01 experiment. This map is then interpolated on a grid of sampling parameter N_s = 512. Here the cosmology is ΛCDM. Bottom: residual between the DEMNUni_cov and COVMOS PDF.