Kantorovich duality for general transport costs and applications
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Publication:2407214
DOI10.1016/j.jfa.2017.08.015zbMath1406.60032arXiv1412.7480OpenAlexW2963942532MaRDI QIDQ2407214
Prasad Tetali, Paul-Marie Samson, Cyril Roberto, Nathael Gozlan
Publication date: 29 September 2017
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1412.7480
Inequalities; stochastic orderings (60E15) Variational problems in a geometric measure-theoretic setting (49Q20) Inequalities involving derivatives and differential and integral operators (26D10) Analytical consequences of geometric convexity (vanishing theorems, etc.) (32F32)
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Cites Work
- Characterization of Talagrand's transport-entropy inequalities in metric spaces
- Optimal transportation under controlled stochastic dynamics
- Concavity of entropy along binomial convolutions
- Displacement convexity of entropy and related inequalities on graphs
- A new characterization of Talagrand's transport-entropy inequalities and applications
- From concentration to logarithmic Sobolev and Poincaré inequalities
- Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution
- The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems
- Modified logarithmic Sobolev inequalities in discrete settings
- Infimum-convolution description of concentration properties of product probability measures, with applications
- A characterization of dimension free concentration in terms of transportation inequalities
- Ricci curvature of Markov chains on metric spaces
- Mass transportation and rough curvature bounds for discrete spaces
- Stochastic optimal control. The discrete time case
- Some deviation inequalities
- The Brunn-Minkowski inequality in Gauss space
- Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
- An isoperimetric inequality on the discrete cube and an elementary proof of the isoperimetric inequality in Gauss space
- Information inequalities and concentration of measure
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
- Hypercontractivity of Hamilton-Jacobi equations.
- Ricci curvature of finite Markov chains via convexity of the entropy
- A function space large deviation principle for certain stochastic integrals
- Concentration of measure inequalities for Markov chains and \(\Phi\)-mixing processes.
- Concentration for locally acting permutations
- Transportation cost-information inequalities and applications to random dynamical systems and diffusions.
- Concentration of measure and isoperimetric inequalities in product spaces
- A measure concentration inequality for contracting Markov chains
- Transportation cost for Gaussian and other product measures
- Ricci curvature for metric-measure spaces via optimal transport
- Transport-entropy inequalities on locally acting groups of permutations
- Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
- Hamilton Jacobi equations on metric spaces and transport entropy inequalities
- The sub-Gaussian constant and concentration inequalities
- A simple proof of duality theorem for Monge-Kantorovich problem
- On the geometry of metric measure spaces. I
- Bounding \(\bar d\)-distance by informational divergence: A method to prove measure concentration
- On Talagrand's deviation inequalities for product measures
- A saddle-point approach to the Monge-Kantorovich optimal transport problem
- Some inequalities satisfied by the quantities of information of Fisher and Shannon
- Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses
- A Topological Application of the Isoperimetric Inequality
- A simple proof of the blowing-up lemma (Corresp.)
- Logarithmic Sobolev Inequalities
- A Curved Brunn--Minkowski Inequality on the Discrete Hypercube, Or: What Is the Ricci Curvature of the Discrete Hypercube?
- Transport Inequalities. A Survey
- The Existence of Probability Measures with Given Marginals
- Partially Alternate Derivation of a Result of Nelson
- Concentration of Measure for the Analysis of Randomized Algorithms
- Optimal Transport
- Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
- New concentration inequalities in product spaces
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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