On quadratic transportation cost inequalities

By Patrick Cattiaux, Arnaud Guillin. 2006

59 citations recorded by the source corpus.

Abstract In this paper we study quadratic transportation cost inequalities. To this end we introduce new families of inequalities (for quadratic transportation cost and for relative entropy) that are shown to be equivalent to the Poincare inequality. This allows us to give some examples of measures satisfying T 2 but not the logarithmic-Sobolev inequality.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/8c301cbe62dd4f4a1a87e305867c5bd1e81eca83

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In Applied Mathematics

Citations in the corpus

Poincaré inequalities and dimension free concentration of measure (2010, methodology): “It was shown by Cattiaux and Guillin in [16] that the implication is strict: there exist probability measures satisfying TC2(·) and not the Logarithmic-Sobolev inequality.”
Semi Log-Concave Markov Diffusions (2013, unknown): “9 in [18] which shows that the inequality W2(hμ, μ) ≤ √”
A characterization of dimension free concentration in terms of transportation inequalities (2008, background): “The case p = 2 was first established by Cattiaux and Guillin in [12] with a completely different proof.”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, unknown): “(1.1)”
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry (2004, background): “For other results in connection with mass transportation, see also [58, 23, 29].”
Transportation-information inequalities for Markov processes (2007, background): “for this conjecture comes from the fact that even for the usual W2Hinequality, the only cases of measures satisfying W2Hbut not log-Sobolev inequality which are known so far have an inﬁnite curvature [9]. That is why in the rest of the paper we are mainly interested in W1I(κ).Nevertheless, note that”
A note on Talagrand’s transportation inequality and logarithmic Sobolev inequality (2008, unknown): “MSC 2000 : 26D10, 47D07, 60G10, 60J60.”