4 problems

Let $\boldsymbol{A},\boldsymbol{B}\rhd 0$ be positive-definite covariance operators on $\mathcal{H}=\mathbb{R}^{d}$, and let $\pi_{\varepsilon}$ and $\pi_{0}$ denote the entropic a…

Let $\rho$ be a compactly supported probability distribution with a density over $\mathbb{R}^d$, and let $\mu=\sum_{j=1}^J\mu_j\delta_{y_j}$ be a discrete measure. Define … where…

Let $\boldsymbol{P}$ and $\boldsymbol{Q}$ be the source and target distributions, let $\boldsymbol{\varepsilon}$ denote the entropic regularization parameter, and let debiasing ref…

Let $(\bm{\pi},\bm{\omega})$ be the limiting trajectory and momentum, and let $\eta=\lim_{n\to\infty}n\,\veps^n$. Zero-regularization conjecture. If $\eta=0$, then the problem desc…