Integral criteria for transportation cost inequalities

Abstract. In this paper, we provide a characterization of a large class of transportation-cost inequalities in terms of exponential integrability of the cost function under the reference probability measure. Our results completely extend the previous works by Djellout, Guillin and Wu (DGW03) and Bolley and Villani (BV03).

[1]  N. Gozlan,et al.  A large deviation approach to some transportation cost inequalities , 2005, math/0510601.

[2]  P. Cattiaux,et al.  DEVIATIONS BOUNDS AND CONDITIONAL PRINCIPLES FOR THIN SETS. , 2005, math/0510257.

[3]  N. Gozlan.  Conditional principles for random weighted measures , 2005 .

[4]  C. Villani,et al.  Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces , 2005, math/0503123.

[5]  C. Villani,et al.  Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities , 2005 .

[6]  Principe conditionnel de Gibbs pour des contraintes fines approchées et inégalités de transport , 2005 .

[7]  A. Guillin,et al.  Transportation cost-information inequalities and applications to random dynamical systems and diffusions , 2004, math/0410172.

[8]  A. Guillin,et al.  Modified logarithmic Sobolev inequalities and transportation inequalities , 2004, math/0405520.

[9]  G. Burton.  TOPICS IN OPTIMAL TRANSPORTATION (Graduate Studies in Mathematics 58) By CÉDRIC VILLANI: 370 pp., US$59.00, ISBN 0-8218-3312-X (American Mathematical Society, Providence, RI, 2003) , 2004 .

[10]  C. Villani.  Topics in Optimal Transportation , 2003 .

[11]  S. Bobkov,et al.  Hypercontractivity of Hamilton-Jacobi equations , 2001 .

[12]  C. Villani,et al.  Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality , 2000 .

[13]  V. Buldygin,et al.  Metric characterization of random variables and random processes , 2000 .

[14]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[15]  M. Talagrand.  Transportation cost for Gaussian and other product measures , 1996 .

[16]  K. Marton.  Bounding $\bar{d}$-distance by informational divergence: a method to prove measure concentration , 1996 .

[17]  Katalin Marton,et al.  A simple proof of the blowing-up lemma , 1986, IEEE Trans. Inf. Theory.