On Talagrand's deviation inequalities for product measures
ESAIM: Probability and Statistics, Tome 1 (1997), pp. 63-87 
@article{PS_1997__1__63_0,
     author = {Ledoux, Michel},
     title = {On {Talagrand's} deviation inequalities for product measures},
     journal = {ESAIM: Probability and Statistics},
     pages = {63--87},
     year = {1997},
     publisher = {EDP Sciences},
     volume = {1},
     mrnumber = {1399224},
     zbl = {0869.60013},
     language = {en},
     url = {https://www.numdam.org/item/PS_1997__1__63_0/}
}
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Ledoux, Michel. On Talagrand's deviation inequalities for product measures. ESAIM: Probability and Statistics, Tome 1 (1997), pp. 63-87. https://www.numdam.org/item/PS_1997__1__63_0/

Aida, S., Masuda, T. and Shigekawa. I, ( 1994), Logarithmic Sobolev inequalities and exponential integrability, J. Funct. Anal. 126 83-101. | Zbl | MR

Bobkov, S. ( 1994), Some extremal properties of Bernoulli distribution, Theory Prob. Appl. to appear. | Zbl | MR

Bobkov, S. ( 1995), On Gross' and Talagrand's inequalities on the discrete cube, Vestnik of Syktyvkar University Ser. 1, 1 12-19 (in Russian). | Zbl | MR

Bobkov, S. Private communication.

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

Dembo, A. ( 1995), Information inequalities and concentration of measure, Ann. Probability, to appear. | Zbl | MR

Dembo, A. and Zeitouni, O. ( 1995), Transportation approach to some concentration inequalities in product spaces, Preprint. | MR

Gromov, M. and Milman, V. D. ( 1983), A topological application of the isoperimetric inequality, Amer. J. Math. 105 843-854. | Zbl | MR

Gross, L. ( 1975), Logarithmic Sobolev inequalities, Amer. J. Math. 97 1061-1083. | Zbl | MR

Holley, R. and Stroock, D. ( 1987), Logarithmic Sobolev inequalities and stochastic Ising models, J. Statist. Phys. 46 1159-1194. | Zbl | MR

Johnson, W. B. and Schechtman, G. ( 1987), Remarks on Talagrand's deviation inequality for Rademacher functions, Longhorn Notes Texas. | Zbl

Kwapień, S. and Szulga, J. ( 1991), Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, Ann. Probability 19 369-379. | Zbl | MR

Ledoux, M. ( 1995), Remarks on logarithmic Sobolev constants, exponential integrability and bounds on the diameter, J. Math. Kyoto Univ. 35 211-220. | Zbl | MR

Ledoux, M. ( 1994), Isoperimetry and Gaussian Analysis, Ecole d'Eté de Probabilités de St-Flour Lecture Notes in Math., Springer-Verlag, to appear. | Zbl | MR

Ledoux, M. and Talagrand, M. ( 1991), Probability in Banach spaces (Isoperimetry and processes), Ergebnisse der Mathematik und ihrer Grenzgebiete Springer-Verlag. | Zbl | MR

Mcdiarmid, C.( 1989), On the method of bounded differences. Surveys in Combinatorics. London Math. Soc. Lecture Notes 141 148-188 Cambridge Univ. Press. | Zbl | MR

Marton, K. ( 1995a), Bounding d-distance by information divergence: a method to prove measure concentration, Ann. Probability, to appear. | Zbl | MR

Marton, K. ( 1995b), A concentration of measure inequality for contracting Markov chains, Geom. and Funct. Anal., to appear. | Zbl

Maurey, B. ( 1991), Some deviations inequalities, Geometric and Funct. Anal. 1 188-197. | Zbl | MR

Milman, V. D. and Schechtman, G. ( 1986), Asymptotic theory of finite dimensional normed spaces, Lecture Notes in Math. 1200 Springer-Verlag. | Zbl | MR

Talagrand, M. ( 1988), An isoperimetric theorem on the cube and the Khintchine-Kahane inequalities, Proc. Amer. Math. Soc. 104 905-909. | Zbl | MR

Talagrand, M. ( 1989), Isoperimetry and integrability of the sum of independent Banach space valued random variables, Ann. Probability 17 1546-1570. | Zbl | MR

Talagrand, M. ( 1994a), Sharper bounds for Gaussian and empirical processes. Ann. Probability 22 28-76. | Zbl | MR

Talagrand, M. ( 1995a), Concentration of measure and isoperimetric inequalities in product spaces, Publications Mathématiques de l'I.H.E.S. 81 73-205. | Zbl | MR | Numdam

Talagrand, M. ( 1994b), A new look at independence, Ann. Probability to appear. | Zbl | MR

Talagrand, M. ( 1995b), New concentration inequalities in product spaces, Invent. math. to appear. | Zbl | MR