@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}, publisher = {EDP-Sciences}, volume = {1}, year = {1997}, mrnumber = {1399224}, zbl = {0869.60013}, language = {en}, url = {http://www.numdam.org/item/PS_1997__1__63_0/} }

Ledoux, Michel. On Talagrand's deviation inequalities for product measures. ESAIM: Probability and Statistics, Volume 1 (1997), pp. 63-87. http://www.numdam.org/item/PS_1997__1__63_0/

Logarithmic Sobolev inequalities and exponential integrability, J. Funct. Anal. 126 83-101. | MR | Zbl

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

( 1994),On Gross' and Talagrand's inequalities on the discrete cube, Vestnik of Syktyvkar University Ser. 1, 1 12-19 (in Russian). | MR | Zbl

( 1995),Private communication.

Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59 335-395. | MR | Zbl

and ( 1984),Information inequalities and concentration of measure, Ann. Probability, to appear. | MR | Zbl

( 1995),Transportation approach to some concentration inequalities in product spaces, Preprint. | MR

and ( 1995),A topological application of the isoperimetric inequality, Amer. J. Math. 105 843-854. | MR | Zbl

and ( 1983),Logarithmic Sobolev inequalities, Amer. J. Math. 97 1061-1083. | MR | Zbl

( 1975),Logarithmic Sobolev inequalities and stochastic Ising models, J. Statist. Phys. 46 1159-1194. | MR | Zbl

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

and ( 1987),Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, Ann. Probability 19 369-379. | MR | Zbl

and ( 1991),Remarks on logarithmic Sobolev constants, exponential integrability and bounds on the diameter, J. Math. Kyoto Univ. 35 211-220. | MR | Zbl

( 1995),Isoperimetry and Gaussian Analysis, Ecole d'Eté de Probabilités de St-Flour Lecture Notes in Math., Springer-Verlag, to appear. | MR | Zbl

( 1994),Probability in Banach spaces (Isoperimetry and processes), Ergebnisse der Mathematik und ihrer Grenzgebiete Springer-Verlag. | MR | Zbl

and ( 1991),On the method of bounded differences. Surveys in Combinatorics. London Math. Soc. Lecture Notes 141 148-188 Cambridge Univ. Press. | MR | Zbl

( 1989),Bounding d-distance by information divergence: a method to prove measure concentration, Ann. Probability, to appear. | MR | Zbl

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

( 1995b),Some deviations inequalities, Geometric and Funct. Anal. 1 188-197. | MR | Zbl

( 1991),Asymptotic theory of finite dimensional normed spaces, Lecture Notes in Math. 1200 Springer-Verlag. | MR | Zbl

and ( 1986),An isoperimetric theorem on the cube and the Khintchine-Kahane inequalities, Proc. Amer. Math. Soc. 104 905-909. | MR | Zbl

( 1988),Isoperimetry and integrability of the sum of independent Banach space valued random variables, Ann. Probability 17 1546-1570. | MR | Zbl

( 1989),Sharper bounds for Gaussian and empirical processes. Ann. Probability 22 28-76. | MR | Zbl

( 1994a),Concentration of measure and isoperimetric inequalities in product spaces, Publications Mathématiques de l'I.H.E.S. 81 73-205. | Numdam | MR | Zbl

( 1995a),A new look at independence, Ann. Probability to appear. | MR | Zbl

( 1994b),New concentration inequalities in product spaces, Invent. math. to appear. | MR | Zbl

( 1995b),