Observed UV luminosity functions (LFs) at low z (left) and high z (right; see Table 1). The shaded areas represent 68% confidence regions at z = 4 and z = 6. The dot-dashed lines show the effects on the LFs at z = 2 and z = 8 of accounting for the full probability distribution of the halo assembly time, which induces a scatter in the galaxy luminosity vs. DM halo mass relation (the inset shows enlargement for z = 2); this scatter has a negligible influence only at redshifts z 4.