Characterization of a class of weak transport-entropy inequalities on the line

By Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Y. Shu, Prasad Tetali. Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2015

49 citations recorded by the source corpus.

We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost function. As an application, we give a necessary and sufficient condition for weak transport-entropy inequalities in dimension one. In particular, we obtain a weak transport-entropy form of the convex Poincar{\'e} inequality in dimension one.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/0cc68d41adcbd441d7d856d3fcabbbd2f59f355a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Applications of weak transport theory (2020, unknown): “The theory for problem (OWT) has been further developed in [1, 34, 33, 45, 44, 46, 29, 32, 6, 9, 7]: Basic results of existence and duality are established in the articles [34, 2, 6].”
On a mixture of Brenier and Strassen Theorems (2018, methodology): “We refer to [30, 29, 64, 65, 20] for works directly connected to [31] and to [63] for an up-to-date survey of applications of weak transport costs to concentration of measure.”
Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems (2017, unknown): “=2 on [0;1] is 1 4 , for a2f p 5; p 5g, one has x 3 = 1 4 and 3 P() = 1 2 (1 =4;0)+ ( 1 . Nevertheless, the situation is strikingly dierent in dimension d= 1 where, according to Gozlan et al. [14] Theorem 1.5, the projection does not depend on %. We are going to explicit this projection by charac”
Existence, duality, and cyclical monotonicity for weak transport costs (2018, background): “The initial works of Gozlan et al. [19, 18] are mainly motivated by applications to geometric inequalities.”