An equivalent condition between Poincaré inequality and \(T_{2}\)-transportation cost inequality

DOI10.1007/s10440-008-9379-zzbMath1193.60026OpenAlexW1975866576MaRDI QIDQ973812

Yu Miao, Zhengliang Zhang

Publication date: 26 May 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-008-9379-z

zbMATH Keywords

Log-Sobolev inequality\(T_{2}\)-transportation inequality

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Inequalities for sums, series and integrals (26D15) Functional inequalities, including subadditivity, convexity, etc. (39B62)

Related Items (3)

Logarithmic Sobolev inequalities for Moebius measures on spheres ⋮ Logarithmic Sobolev inequalities for harmonic measures on spheres ⋮ Beckner inequalities for Moebius measures on spheres

Cites Work

• On quadratic transportation cost inequalities
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Transportation cost inequalities on path spaces over Riemannian manifolds
• Probability distance inequalities on Riemannian manifolds and path spaces.
• Monge-Kantorovitch measure transportation and Monge-Ampère equation on Wiener space
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Hypercontractivity of Hamilton-Jacobi equations.
• Measure transport on Wiener space and the Girsanov theorem.
• Transportation cost inequalities on path and loop groups
• Talagrand's \(T_2\)-transportation inequality w.r.t. a uniform metric for diffusions
• Transportation cost-information inequalities and applications to random dynamical systems and diffusions.
• A measure concentration inequality for contracting Markov chains
• Transportation cost for Gaussian and other product measures
• Talagrand's \(T_2\)-transportation inequality and log-Sobolev inequality for dissipative SPDEs and applications to reaction-diffusion equations
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