We consider random Cayley digraphs of order n with uniformly distributed
generating set of size k. Specifically, we are interested in the asymptotics
of the probability such a Cayley digraph has diameter two as n→∞ and
k=f(n). We find a sharp phase transition from 0 to 1 at around k=nlogn. In particular, if f(n) is asymptotically linear in n, the
probability converges exponentially fast to 1.Comment: 11 page