Monotonicity Properties of Optimal Transportation¶and the FKG and Related Inequalities

By Luis Caffarelli. 2000

267 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/baf40fc93eb7aea72ff4f58b97e21ddc766a569d

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Citations in the corpus

The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems (2004, methodology): “The non-expansivity of T ¼ rj can be rephrased as 0pHess jpId: Of course, it was already noticed by Caffarelli that the non-expansivity of T can be used to ‘‘transport’’ inequalities from g to the measure m: We can also point out that Caffarelli’s result was used to recover Gaussian correlation ineq”
Log-Concavity and Strong Log-Concavity: a review (2014, background): “CorderoErausquin (2002) gave another proof of Hargé’s result, as a consequence of Caffarelli’s Contraction Theorem (for more on the latter theorem, see Section 9.8 below).”
Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order (2013, background): “As noted in [47],Caffarelli’s contraction principle [20] implies that, e.”
Mass Transport and Variants of the Logarithmic Sobolev Inequality (2007, background): “This is related to a simple fact in the spirit of the Caffarelli’s contraction theorem [28].”
On a mixture of Brenier and Strassen Theorems (2018, background): “2, and derive a link with the celebrated Caffarelli’s contraction theorem of [14].”
Stein kernels and moment maps (2018, unknown): “The well-known Caffarelli contraction theorem [9] states that the Brenier map sending the standard Gaussian map onto a uniformly log-concave measure is lipschitz.”
Some Applications of Mass Transport to Gaussian-Type Inequalities (2002, methodology): “Recently,Caffarelli [7] made a crucial observation on the behavior of the Brenier map.”
Marginals of Geometric Inequalities (2007, unknown): “This follows from the methods in [ C -EFM], and was also observed independently by Barthe and Cordero–Erausquin [Ba2].”
A generalization of Caffarelli’s contraction theorem via (reverse) heat flow (2010, unknown): “In the proof of the contraction property of Topt (Theorem 1.3), Caffarelli’s regularity theory for the fully-nonlinear Monge–Ampère equation was an essential ingredient.”
Dealing with moment measures via entropy and optimal transport (2015, methodology): “This requires arguments similar to [8, 9] concerning log-concave measures.”
A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces (2004, background): “As in corollary 6 of [7], the proof is based on a result of [ 7 ] concerning optimal transport of measure.”