Generating and generalizing MSTD sets through Markov processes

The classical More Sums Than Differences (MSTD) problem studies finite sets $A\subset\{0,1,\ldots,n\}$ for which $|A+A|>|A-A|$, where $A+A=\{a_1+a_2:a_1,a_2\in A\}$ and $A-A=\{a_1-a_2:a_1,a_2\in A\}$. As addition is commutative and subtraction is not, it was conjectured that as $n\to\infty$ almost a