Extreme-Value Distributions and Primordial Black-Hole Formation
  We argue that primordial black-hole formation must be described by means of
extreme-value theory. This is a consequence of the large values of the energy
density required to initiate the collapse of black holes in the early Universe
and the finite duration of their collapse. Compared to the Gaussian description
of the most extreme primordial density fluctuations, the holes' mass function
is narrower and peaks towards larger masses. Secondly, thanks to the shallower
fall-off of extreme-value distributions, the predicted abundance of primordial
black holes is boosted by $10^{7}$ orders of magnitude when extrapolating the
observed nearly scale-free power spectrum of the cosmic large-scale structure
to primordial black-hole mass scales.
