Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 3, pp. 331-352. 
@article{AFST_2005_6_14_3_331_0,
     author = {Bolley, Fran\c{c}ois and Villani, C\'edric},
     title = {Weighted {Csisz\'ar-Kullback-Pinsker} inequalities and applications to transportation inequalities},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {331--352},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {3},
     year = {2005},
     mrnumber = {2172583},
     zbl = {1087.60008},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2005_6_14_3_331_0/}
}
TY  - JOUR
AU  - Bolley, François
AU  - Villani, Cédric
TI  - Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2005
SP  - 331
EP  - 352
VL  - 14
IS  - 3
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2005_6_14_3_331_0/
LA  - en
ID  - AFST_2005_6_14_3_331_0
ER  - 
%0 Journal Article
%A Bolley, François
%A Villani, Cédric
%T Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2005
%P 331-352
%V 14
%N 3
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/item/AFST_2005_6_14_3_331_0/
%G en
%F AFST_2005_6_14_3_331_0
Bolley, François; Villani, Cédric. Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 3, pp. 331-352. http://www.numdam.org/item/AFST_2005_6_14_3_331_0/

[1] Blower (G.). - The Gaussian isoperimetric inequality and transportation , Unpublished preprint (2000). | MR | Zbl

[2] Bobkov (S. ), Gentil (I.), Ledoux (M.). - Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl. 80, 7, p. 669-696 (2001). | MR | Zbl

[3] Bobkov (S. ), Götze (F.). - Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal. 163, p. 1-28 (1999). | MR | Zbl

[4] Cattiaux (P. ) , Guillin ( A.). - A criterion for Talagrand's quadratic transportation cost, Preprint (2003). Available at http://arxiv.org/abs/math.PR/ 0312081

[5] Djellout ( H.), Guillin (A.), Wu (L.). - Transportation cost-information inequalities for random dynamical systems and diffusions , Ann. Probab., 32, 3B, p. 2702-2732 (2004). | MR | Zbl

[6] Ledoux (M.). - The concentration of measure phenomenon, vol. 89 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI (2001). | MR | Zbl

[7] Marton (K.). - Bounding @DO>d@FO>-distance by information divergence: a method to prove measure concentration, Ann. Probab. 24, p. 857-866 (1996). | MR | Zbl

[8] Otto (F.) , Villani ( C.). - Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality, J. Funct. Anal. 173, p. 361-400 (2000). | MR | Zbl

[9] Rachev (S.T. ). - Probability metrics and the stability of stochastic models, John Wiley & Sons Ltd., Chichester (1991). | MR | Zbl

[10] Talagrand ( M.). - Transportation cost for Gaussian and other product measures, Geom. Funct. Anal. 6, 3, p. 587-600 (1996). | MR | Zbl

[11] Villani ( C.). - Topics in optimal transportation , vol. 58 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2003). | MR | Zbl