A large deviation approach to some transportation cost inequalities
By Nathael Gozlan, Christian Léonard. 2005
117 citations recorded by the source corpus.
New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. Götze. Their tensorization properties are investigated. Sufficient conditions (and necessary conditions too) for these inequalities are stated in terms of the integrability of the reference measure. Applying these results leads to new deviation results: concentration of measure and deviations of empirical processes.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7a57d541afb81b00c4a9e030b25d126a4c5070ff
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In Applied Mathematics
- Ran Wang
- Xinyu Wang
- Liming Wu
- Nathael Gozlan
- Emmanuel Boissard
- Arnaud Guillin
- Cyril Roberto
- Patrick Cattiaux
In Mathematical Physics
Citations in the corpus
- Sanov’s theorem in the Wasserstein distance: A necessary and sufficient condition (2010, background): “See Gozlan and Léonard (2007) for several important characterizations of (1.5) in terms of concentration inequality (in relation with large deviations exactly), and Bolley et al. (2007) for concentration inequalities about P0(W1(Ln, µ0) > δ)when E = Rd.”
- Bernstein type's concentration inequalities for symmetric Markov processes (2010, unknown): “(1.1)”
- A note on Talagrand’s transportation inequality and logarithmic Sobolev inequality (2008, unknown): “MSC 2000 : 26D10, 47D07, 60G10, 60J60.”
- Characterization of Talagrand's like transportation-cost inequalities on the real line (2006, background): “The interested reader can also find an alternative proof of this result in [10] (see Corollary 1).”
- Poincaré inequalities and dimension free concentration of measure (2010, background): “According to [22], Corollary 1, this latter inequality is equivalent to the transportation-cost inequality TC(ω, a).”