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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Almost Sure Weak Convergence for the Generalized Orthogonal Ensemble
TL;DR: The generalized orthogonal ensemble satisfies isoperimetric inequalities analogous to the Gaussian isoper-imetric inequality, and an analogue of Wigner's law as discussed by the authors.
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A variational approach to some transport inequalities
TL;DR: In this article, an approche des inegalites de transport-entropie fondee sur la minimisation de certaines fonctionnelles definies sur l'espace des mesures de probabilite is proposed.
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Theoretical error performance analysis for variational quantum circuit based functional regression
TL;DR: In this paper , the authors proposed an end-to-end QNN, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression.
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Conditional Expectation, Entropy, and Transport for Convex Gibbs Laws in Free Probability
TL;DR: In this paper, the authors show that conditional expectations and conditional non-microstates free entropy arise as the large limit of the corresponding conditional expectation and entropy for the random matrix models associated to a sufficiently regular convex and semi-concave potential.
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Modified Massive Arratia flow and Wasserstein diffusion
TL;DR: In this article, a variant of the Arratia flow, which consists of a collection of coalescing Brownian motions starting from every point of the unit interval, is presented, where individual particles carry mass which aggregates upon coalescence and scales the diffusivity of each particle in an inverse proportional way.
References
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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.
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.
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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.