  The purpose of this paper is twofold. First, we present a conjecture to the
effect that the ranks of the syzygy modules of a smooth projective variety
become normally distributed as the positivity of the embedding line bundle
grows. Then, in an attempt to render the conjecture plausible, we prove a
result suggesting that this is in any event the typical behavior from a
probabilistic point of view. Specifically, we consider a "random" Betti table
with a fixed number of rows, sampled according to a uniform choice of
Boij-Soderberg coefficients. We compute the asymptotics of the entries as the
length of the table goes to infinity, and show that they become normally
distributed with high probability.
