Luminosity dependence of the conditional ERDF. While our ERDF model given by Equation (15) is independent of halo and black hole properties, the conditional ERDF defined by Equation (17) varies as a function of the bolometric luminosity: higher luminosities are associated with larger Eddington ratios due to the lower number density of high-mass black holes. Shown are the conditional ERDFs for a set of luminosities at z = 0 and (C, θ, λ_c, ρ) = (40, 2, −2, 2).