7 problems

Let $F_0$ be a probability density on $\mathbb{R}^d$, and let $F_1$ be a minimizer of the unconstrained variational problem … Here $S$ is the entropy functional and $W_2$ is the…

Let $\rho,\xi\in\mathcal{P}(\bm{\mathcal{X}})$ and let $\bm{\mu},\bm{\nu}\in\prod_{i=1}^K\mathcal{P}(\mathcal{X}^i)$, with corresponding shadows $\mathcal{S}(\rho;\bm{\mu})$ and…

For Brownian motion on the flat torus, let $W^p$ denote the Wasserstein transportation cost with cost given by the $p$-th power of the flat distance, and let the established upper…

Let $\mathcal D_\infty=\varinjlim \mathcal D_n$, where each $\mathcal D_n$ is endowed with a Wasserstein metric; one may also consider the Wasserstein $p,q$ metric. Wasserstein asy…

Let $\xi_1,\xi_2,\dots,\xi_r$ be the random variables defining the lattice random walk in the preceding estimates, and let $I$ be its index variable. Assume that…

Let $G$ be a second countable compact Hausdorff group with normalized Haar measure … , and set $S_k=\prod_{j=1}^kX_j$. Fix $0<p\leq 1$, a bi-invariant metric on $G$, and a $p$-Höld…

Let $P_0$ be the true distribution, let $P$ denote a posterior draw, let $\mathbb{P}_n$ be the empirical distribution based on $n$ observations, and let $W_p$ be the Wasserstein me…