All Questions

The $p$-Wasserstein between two measures $\nu_1$ and $\nu_2$ on $X$ is given by $$d_p(\nu_{1},\nu_{2})=\left(\underset{\pi\in\Gamma(\nu_{1},\nu_{2})}{\inf}\int_{\mathbf{\mathcal{X}}^{2}}d(x,y)^p\pi(dx,...

For Lebesgue-absolutely continuous probability measures $\rho\ll \mathcal{L}^d$ in the whole space $\mathbb{R}^d$ with finite second moments (i-e $\rho\in \mathcal{P}^2_{ac}(\mathbb{R}^d)$), let $$ \...

Fix a finite first moment probability measure $q\in\mathcal{P}_1(\mathbb R ^d)$, and real numbers $K,M,R$. Consider the following set: $$A:=\left\{p\in\mathcal{P}_1(\mathbb R ^d): \int |x|dp\leq K, \...