Probability distribution of the normalised velocity differences. The blue histogram (bin width = 0.1) displays the distribution Δ_normυ_rad of the difference of the radial velocity differences υ_rad,Gaia − υ_rad,GES normalised by the propagated errors $\sqrt{\sigma {\left[v_{\mathrm{r}\mathrm{a}\mathrm{d},\mathrm{G}\mathrm{a}\mathrm{i}\mathrm{a}}\right]}^2+{\sigma }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}{\left[v_{\mathrm{r}\mathrm{a}\mathrm{d},\mathrm{G}\mathrm{E}\mathrm{S}}\right]}^2}$ where σ_corr[υ_radGES] is the uncertainty corrected according to Babusiaux et al. (2023). The black line is the empirical KDE obtained from the sample distribution. The red line is the probability distribution function (PDF) of a the normal law centred in 0 and of unit variance. The dashed vertical black line indicates the mean of the distribution. The black dotted lines have equation |Δ_normυ_rad| = 2.3 and show where the tails of the empirical distribution become heavier than those of the normal law.