Let x,y,d∈Rnx,y,d\in\mathbb R^nx,y,d∈Rn with d≥0d\geq 0d≥0 be given. A matrix A∈R+n×nA\in\mathbb R_+^{n\times n}A∈R+n×n is column-stochastic when e⊤A=e⊤\mathbb e^\top A=\mathbb e^\tope⊤A=e⊤; it fixes ddd when Ad=dAd=dAd=d. T…
