Top panel: star formation rate density () and luminosity density (ρ_L) derived by integrating the model UV LFs in comparison with the observations before (gray points) and after dust correction (black points). Both ρ_L and are given for (M_AB ⩽ −17.7). Middle: evolution in the stellar mass density (), computed by integrating the stellar mass function to a fixed stellar mass limit of 10⁸ M_☉. Bottom: evolution in the specific star formation rate (sSFR) as a function of redshift for a galaxy with M_* = 5 × 10⁹ M_☉. The red lines show our standard model predictions, while the dashed green lines show the model that includes the full probability distribution of the halo assembly time (i.e., with scatter in the L(M_h, z) relation).