Infimum-convolution description of concentration properties of product probability measures, with applications
Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 3, p. 321-338
@article{AIHPB_2007__43_3_321_0,
     author = {Samson, Paul-Marie},
     title = {Infimum-convolution description of concentration properties of product probability measures, with applications},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {43},
     number = {3},
     year = {2007},
     pages = {321-338},
     doi = {10.1016/j.anihpb.2006.05.003},
     zbl = {1125.60018},
     mrnumber = {2319700},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2007__43_3_321_0}
}
Samson, Paul-Marie. Infimum-convolution description of concentration properties of product probability measures, with applications. Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 3, pp. 321-338. doi : 10.1016/j.anihpb.2006.05.003. http://www.numdam.org/item/AIHPB_2007__43_3_321_0/

[1] S. Aida, T. Masuda, I. Shigekawa, Logarithmic Sobolev inequalities and exponential integrability, J. Func. Anal. 126 (1994) 83-101. | MR 1305064 | Zbl 0846.46020

[2] G. Bennett, Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc. 57 (297) (1962) 33-45. | Zbl 0104.11905

[3] Bernstein, Sur une modification de l'inégalité de Tchebichef, Annals Science Institute SAV. Ukraine, Sect. Math. I (1924).

[4] S. Bobkov, F. Gotze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Func. Anal. 163 (1999) 1-28. | MR 1682772 | Zbl 0924.46027

[5] S. Bobkov, I. Gentil, M. Ledoux, Hypercontractivity of Hamilton-Jacobi equations, Geom. Funct. Anal. 10 (2000) 1028-1052.

[6] S. Boucheron, O. Bousquet, G. Lugosi, P. Massart, Moment inequalities for functions of independent random variables, Ann. Probab. 33 (2005) 514-560. | MR 2123200 | Zbl 1074.60018

[7] S. Boucheron, G. Lugosi, P. Massart, A sharp concentration inequality with applications, Random Structures Algorithms 16 (2000) 277-292. | MR 1749290 | Zbl 0954.60008

[8] S. Boucheron, G. Lugosi, P. Massart, Concentration inequalities using the entropy method, Ann. Probab. 31 (2003) 1583-1614. | MR 1989444 | Zbl 1051.60020

[9] O. Bousquet, A Bennett concentration inequality and its application to suprema of empirical processes, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 495-500. | MR 1890640 | Zbl 1001.60021

[10] O. Bousquet, Concentration inequalities for sub-additive functions using the entropy method, Stochastic Inequalities and Applications 56 (2003) 213-247. | MR 2073435 | Zbl 1037.60015

[11] E.B. Davies, B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Func. Anal. 59 (1984) 335-395. | MR 766493 | Zbl 0568.47034

[12] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, 1964. | JFM 60.0169.01 | Zbl 0010.10703

[13] T. Klein, Une inegalité de concentration à gauche pour les processus empiriques, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 500-505. | MR 1890641 | Zbl 1003.60024

[14] T. Klein, E. Rio, Concentration around the mean for maxima of empirical processes, Ann. Probab. 33 (2005) 1060-1077. | MR 2135312 | Zbl 1066.60023

[15] M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probab. Statist. 1 (1996) 63-87. | Numdam | MR 1399224 | Zbl 0869.60013

[16] M. Ledoux, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, American Mathematical Society, 2001. | MR 1849347 | Zbl 0995.60002

[17] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991. | MR 1102015 | Zbl 0748.60004

[18] G. Lugosi, Concentration-of-measure inequalities, Private communication.

[19] K. Marton, A measure concentration inequality for contracting Markov chains, Geom. Funct. Anal. 6 (1997) 556-571. | MR 1392329 | Zbl 0856.60072

[20] P. Massart, About the constants in Talagrand's concentration inequalities for empirical processes, Ann. Probab. 28 (2000) 863-884. | MR 1782276 | Zbl pre01905939

[21] B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991) 188-197. | MR 1097258 | Zbl 0756.60018

[22] D. Panchenko, A note on Talagrand's concentration inequalities, Electron. Comm. Probab. 6 (2001) 55-65. | MR 1831801 | Zbl 0977.60008

[23] D. Panchenko, Symmetrization approach to concentration inequalities for empirical processes, Ann. Probab. 31 (2003) 2068-2081. | MR 2016612 | Zbl 1042.60008

[24] W. Rhee, M. Talagrand, A sharp deviation inequality for the stochastic traveling salesman problem, Ann. Probab. 17 (1989) 1-8. | MR 972767 | Zbl 0682.68058

[25] E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties, Probab. Theory Related Fields 119 (2000) 163-175. | MR 1818244 | Zbl 0976.60033

[26] E. Rio, Une inégalité de Bennett pour les maxima de processus empiriques, Ann. Inst. H. Poincaré Probab. Statist. 38 (6) (2002) 1053-1058. | Numdam | MR 1955352 | Zbl 1014.60011

[27] P.M. Samson, Concentration inequalities for convex functions on Product Spaces, Progr. Probab. 56 (2003) 33-52. | MR 2073425 | Zbl 1037.60019

[28] M. Schmuckenschlager, Private communication.

[29] M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. Inst. Hautes Études Sci. 81 (1995) 73-205. | Numdam | MR 1361756 | Zbl 0864.60013

[30] M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505-563. | MR 1419006 | Zbl 0893.60001

[31] M. Talagrand, A new look at independence, Ann. Probab. 24 (1996) 1-34. | MR 1387624 | Zbl 0858.60019