SIMBAD references

Given recent X-ray observations of high-redshift active galactic nuclei (AGNs), we consider whether the extreme luminosities of these AGNs are consistent with current semi-analytical models. In particular, we apply extreme-value statistics (EVS) to obtain predictions of extreme X-ray luminosities of AGNs in the redshift range $3\lesssim z\lesssim 6$. We apply this formalism using different X-ray luminosity functions and compare the predicted extreme luminosities to AGNs in the Stripe 82 X-ray catalogue. We find a general consistency between data and the EVS predictions although there is some tension with certain luminosity functions. We discuss possible extensions to this model, including extrapolating our results to even higher redshifts ($z\gtrsim 10$) where AGNs have recently been observed.