82 Citations
Applications of weak transport theory
- MathematicsBernoulli
- 2022
Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali introduced a transport problem for `weak' cost functionals. Basic results of optimal transport theory can be…
Existence, duality, and cyclical monotonicity for weak transport costs
- MathematicsCalculus of Variations and Partial Differential Equations
- 2019
The optimal weak transport problem has recently been introduced by Gozlan et al. (J Funct Anal 273(11):3327–3405, 2017). We provide general existence and duality results for these problems on…
Characterization of a class of weak transport-entropy inequalities on the line
- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2018
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…
On a mixture of Brenier and Strassen Theorems
- MathematicsProceedings of the London Mathematical Society
- 2020
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327–3405).…
Around the entropic Talagrand inequality
- MathematicsBernoulli
- 2020
In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. This class of…
A new class of costs for optimal transport planning
- MathematicsEuropean Journal of Applied Mathematics
- 2018
We study a class of optimal transport planning problems where the reference cost involves a non-linear function G(x, p) representing the transport cost between the Dirac measure δx and a target…
On the convex Poincaré inequality and weak transportation inequalities
- MathematicsBernoulli
- 2019
We prove that for a probability measure on $\mathbb{R}^n$, the Poincar\'e inequality for convex functions is equivalent to the weak transportation inequality with a quadratic-linear cost. This…
Transport Plans with Domain Constraints
- MathematicsApplied Mathematics & Optimization
- 2020
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a…
A Theory of Transfers: Duality and convolution
- Mathematics
- 2018
We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass…
Weak Optimal Entropy Transport Problems
- Computer Science, Mathematics
- 2021
In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero, Mielke, and Savaré…
References
SHOWING 1-10 OF 104 REFERENCES
Weak transport inequalities and applications to exponential and oracle inequalities
- Mathematics
- 2015
We extend the dimension free Talagrand inequalities for convex distance using an extension of Marton’s weak transport to other metrics than the Hamming distance. We study the dual form of these weak…
Optimal transportation under controlled stochastic dynamics
- Mathematics
- 2013
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and…
A characterization of dimension free concentration in terms of transportation inequalities
- Mathematics
- 2009
The aim of this paper is to show that a probability measure concentrates independently of the dimension like a gaussian measure if and only if it verifies Talagrand's $\T_2$ transportation-cost…
A saddle-point approach to the Monge-Kantorovich optimal transport problem
- Mathematics
- 2011
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to $c$-conjugates. A new abstract characterization of the optimal plans is obtained in…
Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
- Mathematics
- 2000
Abstract We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6 , 587–600) for the Gaussian measure, are implied by logarithmic Sobolev…
Displacement convexity of entropy and related inequalities on graphs
- Mathematics
- 2012
We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path…
The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems
- Mathematics
- 2014
We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for…
Ricci curvature for metric-measure spaces via optimal transport
- Mathematics
- 2004
We dene a notion of a measured length space X having nonnegative N-Ricci curvature, for N 2 [1;1), or having1-Ricci curvature bounded below byK, forK2 R. The denitions are in terms of the…
Concentration Inequalities for Convex Functions on Product Spaces
- Mathematics
- 2003
Let µ = µ 1 ⊗ … ⊗ µ n denote a product probability measure on ℝ n with compact support. We present a simple proof to get concentration results for convex functions on ℝ n under µ. We use the infimum…
Ricci Curvature of Finite Markov Chains via Convexity of the Entropy
- Mathematics
- 2012
We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott,…