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.
