Measurable metrics and Gaussian concentration

DOI10.1515/FORUM.2006.020zbMath1101.31012OpenAlexW2078636382MaRDI QIDQ5476393

Francis Hirsch

Publication date: 14 July 2006

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum.2006.020

zbMATH Keywords

entropyWasserstein metriclogarithmic Sobolev inequalityconcentration functionDirichlet formKantorovich metricmeasurable metric

Mathematics Subject Classification ID

Dirichlet forms (31C25) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Stochastic analysis (60H99) Probability theory on linear topological spaces (60B11) Sub-Riemannian geometry (53C17) Functional analysis in probabilistic metric linear spaces (46S50)

Related Items

Transportation cost inequalities on path and loop groups, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations

Cites Work

• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Small-time Gaussian behavior of symmetric diffusion semigroups
• Monge-Kantorovitch measure transportation and Monge-Ampère equation on Wiener space
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• Lipschitz algebras and derivations of von Neumann algebras
• Rademacher's theorem for Wiener functionals
• Bounding \(\bar d\)-distance by informational divergence: A method to prove measure concentration
• Duality theorems for marginal problems
• Logarithmic Sobolev Inequalities
• Nonatomic Lipschitz spaces