Constraints on the correlation between QSO luminosity and host halo mass from high-redshift quasar clustering

Recent measurements of high-redshift QSO clustering from the Sloan Digital Sky Survey indicate that QSOs at z~4 have a bias b~14. We find that this extremely high clustering amplitude, combined with the corresponding space density, constrains the dispersion in the L-Mhalo relation to be less than 50% at 99% confidence for the most conservative case of a 100% duty cycle. This upper limit to the intrinsic dispersion provides as strong a constraint as current upper limits to the intrinsic dispersion in the local M_BH-sigma relation and the ratio of bolometric to Eddington luminosity of luminous QSOs.