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

Recent measurements of high-redshift quasar (QSO) clustering from the Sloan Digital Sky Survey indicate that QSOs at z similar to 4 have a bias < b > similar or equal to 14. We find that this extremely high clustering amplitude, combined with the corresponding space density, constrains the dispersion in the L-M-h relation to be less than 50 per cent at 99 per cent confidence for the most conservative case of a 100 per cent 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.