Characterization of Talagrand's like transportation-cost inequalities on the real line
By Nathael Gozlan. 2006
49 citations recorded by the source corpus.
Abstract In this paper, we give necessary and sufficient conditions for Talagrand's like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimension-free concentration of measure property. Another byproduct is the characterization of modified Log-Sobolev inequalities for log-concave probability measures on R .
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/8e89b2ec5ea3c9759a905f4870edcaabb77f98e1
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In Applied Mathematics
- Nathael Gozlan
- Arnaud Guillin
- Patrick Cattiaux
- Christian Léonard
- Cyril Roberto
- Liming Wu
- Nian Yao
- Sourav Chatterjee
Citations in the corpus
- Applications of Stein's method for concentration inequalities (2009, background): “Also in [5, 21, 22], the authors deal with tails (possibly) larger than Gaussian.”
- Poincaré inequalities and dimension free concentration of measure (2010, methodology): “This technique was previously used by the author in [21] to characterize a large class of transportation-cost inequalities on the real line.”
- Transportation-information inequalities for Markov processes (2007, background): “Cattiaux and Guillin [9] constructed the first example for which Talagrand’s transportation inequality holds but not log-Sobolev inequality, and Gozlan [23] found a necessary and sufficient condition for Talagrand’s transportation inequality with µ(dx) = e−V (x)dx on R when the Bakry-Emery curvature”
- Transport Inequalities. A Survey (2010, background): “In [50], Gozlan recovered Cattiaux and Guillin’s sufficient condition (45) for T2 and extended it to other transport-entropy inequalities on the real axis.”
- Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry (2010, methodology): “One is based on the Lyapunov function approach [4; 30; 3], the other is based on mass transportation method [35; 36] (see also [15; 54; 20; 22]).”