Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Felix Otto,Cédric Villani +1 more
Reads0
Chats0
TLDR
In this paper, it was shown that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587-600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities.About:
This article is published in Journal of Functional Analysis.The article was published on 2000-06-01 and is currently open access. It has received 1080 citations till now. The article focuses on the topics: Sobolev inequality & Interpolation inequality.read more
Citations
More filters
Journal ArticleDOI
Complete logarithmic Sobolev inequalities via Ricci curvature bounded below
TL;DR: In this paper , it was shown that for a symmetric Markov semigroup, Ricci curvature bounded from below by a non-positive constant combined with a finite L∞-mixing time implies the modified log-Sobolev inequality.
Journal ArticleDOI
Logarithmic Sobolev inequalities for Moebius measures on spheres
TL;DR: In this article, the optimal Poincaré constant is not greater than 2 n - 2 (n ≥ 3 {n\\geq 3} ) and the optimal logarithmic Sobolev constant is strictly stronger than L 2 {L^{2}} -transportation-information inequalities.
Journal ArticleDOI
Dimensional contraction via Markov transportation distance
TL;DR: In this paper, it was shown that curvature conditions a la Bakry-Emery are equivalent to contraction properties of the heat semigroup with respect to the classical quadratic Wasserstein distance.
Dissertation
Le problème de Schrödinger et ses liens avec le transport optimal et les inégalités fonctionnelles
TL;DR: In this article, the authors consider the problem of minimization of the entropy of the flux de chaleur in the context of diffusion and show how to solve it using the theory of the transport optimal.
Posted Content
Instability Results for the Logarithmic Sobolev Inequality and its Application to the Beckner--Hirschman Inequality
TL;DR: In this paper, the stability bounds for the logarithmic Sobolev inequality with respect to probability measures with bounded second moments are shown to be the best possible for any probability measure.
References
More filters
Book
Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
Journal ArticleDOI
Polar Factorization and Monotone Rearrangement of Vector-Valued Functions
TL;DR: In this paper, it was shown that for every vector-valued function u Lp(X, p; Rd) there is a unique polar factorization u = V$.s, where $ is a convex function defined on R and s is a measure-preserving mapping from (x, p) into (Q, I. I), provided that u is nondegenerate.
Journal ArticleDOI
The geometry of dissipative evolution equations: the porous medium equation
TL;DR: In this paper, the authors show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural, and they use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
Book
Topological methods in hydrodynamics
Vladimir I. Arnold,Boris Khesin +1 more
TL;DR: A group theoretical approach to hydrodynamics is proposed in this article, where the authors consider the hydrodynamic geometry of diffeomorphism groups and the principle of least action implies that the motion of a fluid is described by geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy.
Journal ArticleDOI
The variational formulation of the Fokker-Planck equation
TL;DR: The Fokker-Planck equation as mentioned in this paper describes the evolution of the probability density for a stochastic process associated with an Ito Stochastic Differential Equation.