The Formation Probability of Primordial Black Holes
  We calculate the exact formation probability of primordial black holes
generated during the collapse at horizon re-entry of large fluctuations
produced during inflation, such as those ascribed to a period of
ultra-slow-roll. We show that it interpolates between a Gaussian at small
values of the average density contrast and a Cauchy probability distribution at
large values. The corresponding abundance of primordial black holes may be
larger than the Gaussian one by several orders of magnitude. The mass function
is also shifted towards larger masses.
