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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Strong posterior contraction rates via Wasserstein dynamics
TL;DR: In this paper , a new approach to posterior contractions rates (PCRs) for both parametric and nonparametric (nonparametric) Bayesian models is presented, which combines an assumption of local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the Wasserstein distance, referred to as Wassersteinsign.
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Optimal transportation, topology and uniqueness
TL;DR: In this article, Hestir and Williams' necessary and sufficient condition on the support of a joint probability to guarantee extremality among all measures which share its marginals is discussed.
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Wasserstein information matrix
TL;DR: Wasserstein information matrices (WIMs) as discussed by the authors are the analogs of classical Fisher matrices for statistical models, and they have been shown to have asymptotic behaviors and efficiency for Wasserstein natural gradients.
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Variance reduction for dependent sequences with applications to Stochastic Gradient MCMC
TL;DR: A novel and practical variance reduction approach for additive functionals of dependent sequences that combines the use of control variates with the minimisation of an empirical variance estimate and derives finite-time bounds of the excess asymptotic variance to zero.
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TCI for SDEs with irregular drifts
TL;DR: For stochastic differential equations with Dini continuous drift and singular coefficients, this paper obtained a lower bound of Ω(T_2(C) ), where T is the number of singular coefficients.
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.