  Lazarev, Miller and O'Bryant investigated the distribution of $|S+S|$ for $S$
chosen uniformly at random from $\{0, 1, \dots, n-1\}$, and proved the
existence of a divot at missing 7 sums (the probability of missing exactly 7
sums is less than missing 6 or missing 8 sums). We study related questions for
$|S-S|$, and shows some divots from one end of the probability distribution,
$P(|S-S|=k)$, as well as a peak at $k=4$ from the other end, $P(2n-1-|S-S|=k)$.
A corollary of our results is an asymptotic bound for the number of complete
rulers of length $n$.
