From concentration to logarithmic Sobolev and Poincaré inequalities

DOI10.1016/j.jfa.2010.11.010zbMath1226.60024OpenAlexW2065181876MaRDI QIDQ629718

Nathael Gozlan, Paul-Marie Samson, Cyril Roberto

Publication date: 9 March 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.11.010

zbMATH Keywords

Ricci curvatureconcentration of measurePoincaré inequalitieslogarithmic-Sobolev inequalitieslength spacestransport inequalities

Mathematics Subject Classification ID

Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Diffusion processes and stochastic analysis on manifolds (58J65) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Measures and integrals in product spaces (28A35)

Related Items (12)

A note on transportation cost inequalities for diffusions with reflections ⋮ Kantorovich duality for general transport costs and applications ⋮ Characterization of Talagrand's transport-entropy inequalities in metric spaces ⋮ Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds ⋮ Note on the q-logarithmic Sobolev and p-Talagrand inequalities on Carnot groups ⋮ A variational approach to some transport inequalities ⋮ Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature ⋮ Functional inequalities and Hamilton-Jacobi equations in geodesic spaces ⋮ Transport proofs of some discrete variants of the Prékopa-Leindler inequality ⋮ Estimates of eigenvalues of the Laplacian by a reduced number of subsets ⋮ From dimension free concentration to the Poincaré inequality ⋮ Talagrand concentration inequalities for stochastic partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new characterization of Talagrand's transport-entropy inequalities and applications
• Super Poincaré inequalities, Orlicz norms and essential spectrum
• Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
• Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups
• Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
• Modified log-Sobolev inequalities and isoperimetry
• Mass transport and variants of the logarithmic Sobolev inequality
• A characterization of dimension free concentration in terms of transportation inequalities
• Isoperimetric and concentration inequalities: equivalence under curvature lower bound
• Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Some applications of mass transport to Gaussian-type inequalities
• Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Isoperimetric and analytic inequalities for log-concave probability measures
• Hypercontractivity of Hamilton-Jacobi equations.
• A generalization of Poincaré and log-Sobolev inequalities
• Transportation cost-information inequalities and applications to random dynamical systems and diffusions.
• Geometric inequalities via a general comparison principle for interacting gases
• Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
• Functional inequalities for empty essential spectrum
• Hamilton-Jacobi semigroup on length spaces and applications
• Ricci curvature for metric-measure spaces via optimal transport
• Integral criteria for transportation-cost inequalities
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• A large deviation approach to some transportation cost inequalities
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• A simple proof of the blowing-up lemma (Corresp.)
• A Generalized Poincare Inequality for Gaussian Measures
• Logarithmic Sobolev Inequalities
• A Simple Analytic Proof of an Inequality by P. Buser
• Spectral gap for hyperbounded operators
• On the role of convexity in functional and isoperimetric inequalities
• On Isoperimetric Constants for Log-Concave Probability Distributions
• Optimal Transport
• The geometry of Markov diffusion generators

This page was built for publication: From concentration to logarithmic Sobolev and Poincaré inequalities