List questions from optimal-transport

Published on 21 May 2022 - 6:01

41

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Embedding $X \ni x \mapsto \delta_x \in P_2(X)$ is totally convex

Published on 23 May 2022 - 13:43

193

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Is the composition of two optimal transport maps still optimal (under some assumptions)?

Published on 10 Jun 2022 - 17:21

51

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Derivative of Kantorovic Potential wrt to Measure

Published on 23 Feb 2026 - 12:07

115

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Optimal objective of Static Schrodinger Bridge

Published on 23 Jun 2022 - 6:17

265

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Knott-Smith optimality

Published on 28 Jun 2022 - 19:02

2.4k

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Brenier theorem on optimal transport

Published on 03 Jul 2022 - 16:28

65

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Is the $c$-transform $f^c$ defined by $f^c(y) := \inf_{x\in X} [c(x, y)- f(x)]$ measurable?

Published on 23 Feb 2026 - 12:08

139

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Kantorovich-Rubinstein theorem

Published on 08 Jul 2022 - 0:15

88

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Let $p \in [1, +\infty)$. Then $\mu_m \overset{\ast}{\rightharpoonup} \mu$ if and only if $W_p (\mu_m, \mu) \to 0$

Published on 09 Jul 2022 - 4:56

145

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About optimal transport

Published on 09 Jul 2022 - 17:55

43

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$W_p (\mu_m, \mu) \to 0$ if and only if $\mu_m \overset{\ast}{\rightharpoonup} \mu$ and $\int_X |x|^p \mathrm d \mu_m \to \int_X |x|^p \mathrm d \mu$

Published on 09 Jul 2022 - 20:02

379

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Gluing lemma in optimal transport

Published on 10 Jul 2022 - 2:05

478

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Wasserstein metric satisfies triangle inequality

Published on 10 Jul 2022 - 3:22

53

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What is the result of the following integral including Wasserstein distance?

Published on 10 Jul 2022 - 7:20

List Question

What functions are continuous in the Wasserstein metric?

Embedding $X \ni x \mapsto \delta_x \in P_2(X)$ is totally convex

Is the composition of two optimal transport maps still optimal (under some assumptions)?

Derivative of Kantorovic Potential wrt to Measure

Optimal objective of Static Schrodinger Bridge

Knott-Smith optimality

Brenier theorem on optimal transport

Is the $c$-transform $f^c$ defined by $f^c(y) := \inf_{x\in X} [c(x, y)- f(x)]$ measurable?

Kantorovich-Rubinstein theorem

Let $p \in [1, +\infty)$. Then $\mu_m \overset{\ast}{\rightharpoonup} \mu$ if and only if $W_p (\mu_m, \mu) \to 0$

About optimal transport

$W_p (\mu_m, \mu) \to 0$ if and only if $\mu_m \overset{\ast}{\rightharpoonup} \mu$ and $\int_X |x|^p \mathrm d \mu_m \to \int_X |x|^p \mathrm d \mu$

Gluing lemma in optimal transport

Wasserstein metric satisfies triangle inequality

What is the result of the following integral including Wasserstein distance?

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