Relative volume of comparable pairs under semigroup majorization

Fabio Deelan Cunden, Jakub Czartowski, Giovanni Gramegna +1

Any semigroup $\mathcal{S}$ of stochastic matrices induces a semigroup majorization relation ${\prec }^{\mathcal{S}}$ on the set ${\Delta }_{n-1}$ of probability $n$-vectors. Pick $X,Y$ at ra…