Exact Extreme Value Statistics and the Halo Mass Function

Motivated by observations that suggest the presence of extremely massive clusters at uncomfortably high redshifts for the standard cosmological model to explain, we develop a theoretical framework for the study of the most massive haloes, e.g. the most massive cluster found in a given volume, based on Extreme Value Statistics (EVS). We proceed from the exact distribution of the extreme values drawn from a known underlying distribution, rather than relying on asymptotic theory (which is independent of the underlying form), arguing that the former is much more likely to furnish robust statistical results. We illustrate this argument with a discussion of the use of extreme value statistics as a probe of primordial non-Gaussianity.