All Questions

There are many possible metrics one can place on the space of Gaussian probability measures on $\mathbb{R}^n$, with strictly positive definite co-variance matrices. Let's denote this space by $X$. I'...

In the article "Wasserstein Geometry Of Gaussian Measures" by Asuka Takatsu the author shows how the space of d-dimensional Gaussian probability measures with non-singular covariance ...

I know there are concentration bounds on $W(\mu,\hat{\mu})$ where $\mu$ and $\hat{\mu}$ are true and empirical distributions respectively, but is there anything out there on $W(\mu,\nu)$ versus $W(\...

Let $(X,Y)$ be a pair of random variables on a measure space $\mathcal T \subseteq \text{"subsets of }\mathbb R^2\text{"}$, with joint probability distribution $P$. We don't assume $X$ and $Y$ are ...

I was wondering whether one has studied the Bregman divergence arising from a squared Wasserstein distance. More precisely, let $\Omega\subset \mathbb{R}^d$ be a compact set and $c\in \Omega\times \...

We consider the two distributions $$ p_t = p_0 * N(0, tI),\quad q_t = q_0 * N(0, t I), $$ where $*$ denotes the convolution between two densities, while $p_0$ and $q_0$ have the same mean and ...