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Recent measurements of high‐redshift quasar (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 – 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 –σ  relation and the ratio of bolometric to Eddington luminosity of luminous QSOs.

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