Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Felix Otto,Cédric Villani +1 more
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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
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The entropy method under curvature-dimension conditions in the spirit of Bakry-Emery in the discrete setting of Markov chains
Frederic Weber,Rico Zacher +1 more
TL;DR: In this article, the authors consider continuous-time Markov chains on discrete spaces and identify a curvature-dimension inequality, the condition C D ϒ ( κ, ∞ ), which serves as a natural analogue of the classical Bakry-Emery condition in several respects.
On the Lipschitz properties of transportation along heat flows
Dan Mikulincer,Yair Shenfeld +1 more
TL;DR: In this paper , the authors prove new Lipschitz properties for transport maps along heat-ows, constructed by Kim and Milman, for (semi)-log-concave measures and Gaussian mixtures.
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Optimal Multiphase Transportation with prescribed momentum
Yann Brenier,Marjolaine Puel +1 more
TL;DR: In this article, a multiphase generalization of the Monge-Kantorovich optimal transportation problem is addressed, and the existence of optimal solutions is established; the optimality equations are related to classical Electrodynamics.
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On the trend to global equilibrium for Kuramoto Oscillators
Javier Morales,David Poyato +1 more
TL;DR: In this paper, the convergence of the Kuramoto-Sakaguchi equation to the stable equilibrium was studied in a large coupling strength regime from generic initial data using the stability of the equation in the Wasserstein distance, and the rate at which discrete Kuramoto oscillators concentrate around the global equilibrium.
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Asymptotics for semi-discrete entropic optimal transport
TL;DR: In this article, exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete (C2D) setting were derived for the case of continuous-continuous (C3D) problems.
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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.
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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.
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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.
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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.
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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.