All Questions
Tagged with wasserstein analysis
4
questions
0
votes
0
answers
21
views
Regularity of Kantorovich potentials for general cost function
I know De Philippis and Figalli have a paper studying the regularity of the Kantorovich potential. In Theorem 3.3, the authors show that the potential is $C^{k+2, \beta}$ if the density functions of ...
- 11
0
votes
0
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18
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Showing that a minimzing sequence for the Wasserstein Variance functional must be tight
I am trying to understand this 2011 paper by Agueh & Carlier [https://www.ceremade.dauphine.fr/~carlier/AC_bary_Aug11_10.pdf] where they introduce the notion of barycenter in the 2-Wasserstein ...
- 11
3
votes
1
answer
477
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Quantitative bound on Wasserstein distances by $L^p$ distances?
Given two smooth probability densities $f$ and $g$ on $\mathbb{R}$ (or $\mathbb{R}_+$) with finite $p$-th moments. I am wondering if anyone is aware of some explicit upper bound on $W_p(f,g)$ in terms ...
- 2,860
1
vote
1
answer
176
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What is the p-th moment finite in the definition of Wasserstein space?
I am confused about the following notation:
For a simple case, let $X=R^d$ or $X=R$. What dose
$$
\int_X \|x\|^pd\mu(x)
$$
mean for a Borel probability measure $\mu$?
For $X=R$, then $x\in R$ is a 1-...
- 1,520