Some Applications of Mass Transport to Gaussian-Type Inequalities

By Dario Cordero-Erausquin. 2002

145 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a73a53842444f82be77287a4ba2c6a7303c1ff11

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In Applied Mathematics

Citations in the corpus

On a mixture of Brenier and Strassen Theorems (2018, background): “This important result has numerous applications in the field of functional inequalities [32, 17, 55].”
Mass Transport and Variants of the Logarithmic Sobolev Inequality (2007, background): “We apply the manifold version of (4) obtained by Cordero-Erausquin, McCann and Schmuckenschläger in [36] for quadratic transportation cost.”
Moment Measures (2013, methodology): “More specifically, we will exploit here the differential point view used in [8] to prove logarithmic-Sobolev inequalities.”
Quantitative logarithmic Sobolev inequalities and stability estimates (2014, methodology): “Following [13], H(ν) ≥ 1 2 W2(ν, γ) 2 + ∫”
Hypercontractivity of Hamilton-Jacobi equations (2001, methodology): “The proof relies on a general HWI inequality involving the entropyH , the Wasserstein distance W2 and the Fisher information I which may be established using the Brenier–McCann mass transportation by the gradient of a convex function (see [12,24] and the references therein).”
Transport Inequalities. A Survey (2010, background): “This section is devoted to some results which have been proved by Cordero-Erausquin in [27] and Cordero-Erausquin, Gangbo and Houdré in [28].”
On Kac's chaos and related problems (2012, background): “16) has been proved in [55], see also [65, 66, 54, 9, 21].”
Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport (2006, methodology): “The form of this inequality already suggests the fundamental result (26) of [ 13 ] and the preceding section.”
A generalization of Caffarelli’s contraction theorem via (reverse) heat flow (2010, unknown): “We refer to [17,25,50] and the references therein for the history of this conjecture, which remains open for n ≥ 3.”
A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces (2004, background): “Other correlation inequalities concerning log-concave functions or ”decreasing” functions could be found in the papers of Pitt [27], Bakry and Michel [1], Schechtman , Schlumprecht and Zinn [30], Harg´ e [15], Szarek and Werner [35], Cordero-Erausquin [ 11 ] (see those papers for further references)”
The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems (2004, methodology): “We can also point out that Caffarelli’s result was used to recover Gaussian correlation inequalities in [9].”
Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half‐spaces via mass transport and consequences (2013, methodology): “Another proof of the sharp Lp-logarithmic Sobolev inequality for all p 1 is given in [3] and in [11] where the authors exploit the mass transportation method.”
Triangular transformations of measures (2005, methodology): “For n = 1 and g = 1 the established equality (naturally, without traces and determinants) is present in the reasoning in [21], and in [9] a close argumentation with the use of Taylor’s formula is employed in the derivation of an inequality for some optimal mappings.”
On quadratic transportation cost inequalities (2006, background): “[18,4,26] (see also [12]) If μ satisfies the logarithmic-Sobolev inequality (L.”