The logarithmic Sobolev inequality for the Wasserstein diffusion

DOI10.1007/s00440-008-0166-6zbMath1173.58014OpenAlexW2082645259MaRDI QIDQ839418

Wilhelm Stannat, Maik Döring

Publication date: 2 September 2009

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-008-0166-6

zbMATH Keywords

entropyDirichlet formWasserstein diffusionLogarithmic Sobolev inequality

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Markov semigroups and applications to diffusion processes (47D07) Diffusion processes and stochastic analysis on manifolds (58J65) Spaces of measures, convergence of measures (28A33) Transition functions, generators and resolvents (60J35)

Related Items (9)

The Dirichlet-Ferguson diffusion on the space of probability measures over a closed Riemannian manifold ⋮ Functional Inequalities for the Wasserstein Dirichlet Form ⋮ Entropic Measure on Multidimensional Spaces ⋮ A Monotone Approximation to the Wasserstein Diffusion ⋮ Reversible coalescing-fragmentating Wasserstein dynamics on the real line ⋮ A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval ⋮ Dean-Kawasaki dynamics: ill-posedness vs. triviality ⋮ Transportation cost inequalities for Wasserstein diffusions ⋮ Particle approximation of the Wasserstein diffusion

Cites Work

• Unnamed Item
• Dirichlet forms and symmetric Markov processes
• Long-time behaviour and regularity properties of transition semigroups of Fleming-Viot processes
• On the validity of the log-Sobolev inequality for symmetric Fleming-Viot operators.
• Entropic measure and Wasserstein diffusion
• Functional inequalities for uniformly integrable semigroups and application to essential spectrums
• Fleming–Viot Processes in Population Genetics

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