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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Global fluctuations for 1D log-gas dynamics
TL;DR: In this paper, the authors studied the hydrodynamic limit in the themacroscopic regime of the coupled system of stochastic differential equations, and proved that the fluctuations around the limit are Gaussian and satisfy an explicit PDE.
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Kernelized Wasserstein Natural Gradient
TL;DR: This work proposes a general framework to approximate the natural gradient for the Wasserstein metric, by leveraging a dual formulation of the metric restricted to a Reproducing Kernel Hilbert Space, and leads to an estimator for gradient direction that can trade-off accuracy and computational cost, with theoretical guarantees.
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A Brascamp-Lieb type covariance estimate
TL;DR: In this article, a new covariance estimate was derived for ferromagnetic Gaussian measures, which has a similar structure as the Brascamp-Lieb inequality and is optimal for Ferromagnetworks.
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Equivalence of a mixing condition and the LSI in spin systems with infinite range interaction
Christopher Henderson,Georg Menz +1 more
TL;DR: In this paper, a new technique for deducing decay of correlations from a uniform Poincare inequality based on a directional PoINCare inequality was developed through an averaging procedure, which is equivalent to the Dobrushin-Shlosman mixing condition.
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Stochastic Volterra equations driven by fractional Brownian motion
Xiliang Fan,Xiliang Fan +1 more
TL;DR: In this paper, a class of stochastic Volterra equations driven by fractional Brownian motion was studied and the Driver type integration by parts formula and shift Harnack type inequalities were established.
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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.