2 problems

Let $t\mapsto\bm{\pi}_t$ be the limit trajectory of couplings, and let $\pi_\infty$ be a stationary coupling. For a cost $c(x,y)=h(x-y)$ with strictly convex…

Let $bc,bd\top\to\to$ be probability measures in $a9_1(a1)$, and consider couplings $(X,Y)$ with law in $a0(bc,bd)$ satisfying $X\textleq Y$. Excursion coupling conjecture. Among a…