Mixture coupling & $W_2^2$

An upper bound, stage by stage.

Indexing convention

i = source index · $A_i,\ \pi_i$

j = target index · $Q_j,\ \rho_j$

γ_ij = mass sent from source $A_i$ to target $Q_j$

Colour

source $A_i$ ($\pi$)

target $Q_j$ ($\rho$)

transport