Text Many questions in additive number theory (Goldbach's conjecture, Fermat's Last
Theorem, the Twin Primes conjecture) can be expressed in the language of sum and
difference sets. As a typical pair contributes one sum and two differences, we expect| A− A|>|
A+ A| for finite sets A. However, Martin and O'Bryant showed a positive proportion of subsets
of {0,…, n} are sum-dominant. We generalize previous work and study sums and differences
of pairs of correlated sets (A, B)(a∈{0,…, n} is in A with probability p, and a goes in B with …

… Correlated Random Pairs All of the literature to date has looked at sums and differences
of a set with itself. … All of the literature to date has looked at sums and differences of a set
with itself. …