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
Convexity inequalities and optimal transport of infinite-dimensional measures
TL;DR: In this paper, the authors generalize Talagrand's inequality in the theory of optimal transport and give some applications of their result in particular for a couple of transportation mappings.
Posted Content
Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities
TL;DR: For a symmetric markov process, the authors showed that the spectral gap in the space of Lipschitz functions for a diffusion process implies the usual transportation inequalities (W_pH) and the corresponding concentration inequalities for the invariant measure.
Journal ArticleDOI
Transportation inequalities for stochastic differential equations of pure jumps
TL;DR: In this article, a differentielle stochastique de pur saut, bien que l’inegalite de Poincare ne soit pas valide en general, nous pouvons quand meme etablir, sous la condition de dissipativite, des inegalites de transport W1H pour sa mesure invariante et pour sa loi (au niveau de processus) sur l'espace des trajectoires cadlag, muni de la metrique L1 ou d'une
Journal ArticleDOI
Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump
TL;DR: In this article, a generalized version of the Harnack inequality for generalized Mehler semigroups with jump is presented. And the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroup with jump.
Posted Content
Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions
TL;DR: In this article, the authors prove a version of Talagrand's concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry.
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.