Random pro-p groups, braid groups, and random tame Galois groups
  We introduce a heuristic prediction for the distribution of the isomorphism class of the Galois group of the maximal pro-p extension of Q unramified outside a "random" set of primes. This is guided by reasoning similar to that governing the Cohen-Lenstra conjectures. We conclude by describing theoretical and experimental evidence for our heuristic. 
Nigel Boston and Jordan S. Ellenberg
math.GR math.NT