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We argue that primordial black-hole formation must be described by means ofextreme-value theory. This is a consequence of the large values of the energydensity required to initiate the collapse of black holes in the early Universeand the finite duration of their collapse. Compared to the Gaussian descriptionof the most extreme primordial density fluctuations, the holes' mass functionis narrower and peaks towards larger masses. Secondly, thanks to the shallowerfall-off of extreme-value distributions, the predicted abundance of primordialblack holes is boosted by $10^{7}$ orders of magnitude when extrapolating theobserved nearly scale-free power spectrum of the cosmic large-scale structureto primordial black-hole mass scales.

Extreme-Value Distributions and Primordial Black-Hole Formation