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Results tagged with optimal-transportation
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user 42644
7
votes
2
answers
3k
views
The largest Wasserstein distance to uniform distribution among all probability distributions...
I am looking for the largest Wasserstein distance to the uniform distribution among all probability distributions with uniform marginals.
More specifically, let $\Xi=\{1,2,\ldots,N\}^2$, and let $\nu …
- 422
6
votes
Accepted
Wasserstein interpolation between two probability measures on a metric space
The following discussion is based on the book Gradient Flows by Ambrosio, Gigli, and Savare (2008).
Consider $p$-Wasserstein distance with $p>1$ on a Hilbert space (for the sake of uniqueness). Let $ …
- 422
2
votes
1
answer
181
views
Strong convexity of internal energy with respect to Wasserstein metric
It is well known that the internal energy (see, e.g., Definition 3.32 in and Proposition 3.33 in 1) is geodesically convex with the 2-Wasserstein distance. I was wondering under what condition, the in …
- 422