Extreme value statistics PDF as a function of the Eddington ratio for a GN-z11-like AGN. Blue solid line shows the best-fit Gaussian (reduced ${\chi }_{\nu }^2=1.4$) to the Eddington ratio distribution from the V21 simulation for BHs in the redshift range 10 < z < 11 and M_BH > 10⁶ M_⊙. The peak of the best fit is around λ_Edd ∼ 0.25. The dashed (dotted) red (green) line represents the EVS for the largest (smallest) considered value of m₁ (see text). The orange solid line (shaded region) shows the GN-z11 Eddington ratio (1σ uncertainty) estimated by Maiolino et al. (2024).