  For any finite set of integers X, define its sumset X+X to be {x+y: x, y in
X}. In a recent paper, Martin and O'Bryant investigated the distribution of
|A+A| given the uniform distribution on subsets A of {0, 1, ..., n-1}. They
also conjectured the existence of a limiting distribution for |A+A| and showed
that the expectation of |A+A| is 2n - 11 + O((3/4)^{n/2}). Zhao proved that the
limits m(k) := lim_{n --> oo} Prob(2n-1-|A+A|=k) exist, and that sum_{k >= 0}
m(k)=1.
  We continue this program and give exponentially decaying upper and lower
bounds on m(k), and sharp bounds on m(k) for small k. Surprisingly, the
distribution is at least bimodal; sumsets have an unexpected bias against
missing exactly 7 sums. The proof of the latter is by reduction to questions on
the distribution of related random variables, with large scale numerical
computations a key ingredient in the analysis. We also derive an explicit
formula for the variance of |A+A| in terms of Fibonacci numbers, finding
Var(|A+A|) is approximately 35.9658. New difficulties arise in the form of weak
dependence between events of the form {x in A+A}, {y in A+A}. We surmount these
obstructions by translating the problem to graph theory. This approach also
yields good bounds on the probability for A+A missing a consecutive block of
length k.
