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• W1979732034 abstract "This paper is devoted to the concentration properties of product probability measures μ=μ1⊗⋯⊗μn, expressed in term of dimension-free functional inequalities of the form(∫eαQαfdμ)1α(∫e−(1−α)fdμ)1(1−α)⩽1, where α is a parameter, 0<α<1, and Qαf is an appropriate infimum-convolution operator. This point of view has been introduced by Maurey [B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991) 188–197]. It has its origins in concentration inequalities by Talagrand where the enlargement of sets is done in accordance with the cost function of the operator Qαf (see [M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. Inst. Hautes Études Sci. 81 (1995) 73–205, M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505–563, M. Talagrand, A new look at independence, Ann. Probab. 24 (1996) 1–34]). A main application of the functional inequalities obtained here is optimal deviations inequalities for suprema of sums of independent random variables. As example, we also derive classical deviations bounds for the one-dimensional bin packing problem. Cet article est consacré à l'étude de propriétés de concentration des probabilités produit μ=μ1⊗⋯⊗μn, en termes d'inégalités fonctionnelles indépendantes de la dimension, de la forme(∫eαQαfdμ)1α(∫e−(1−α)fdμ)1(1−α)⩽1, où α est un paramètre 0<α<1, et Qαf est un opérateur d'infimum-convolution approprié. Ce point de vue a été introduit par Maurey [B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991) 188–197]. Il tient ses origines dans des inégalités de concentration de Talagrand, pour lesquelles l'élargissement des ensembles est lié à la fonction de coût de l'opérateur Qαf (voir [M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. Inst. Hautes Études Sci. 81 (1995) 73–205, M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505–563, M. Talagrand, A new look at independence, Ann. Probab. 24 (1996) 1–34]). Comme application majeure de ces inégalités fonctionnelles, nous obtenons des inégalités de déviations optimales pour les supréma de sommes de variables aléatoires indépendantes. Par ailleurs, à titre d'exemple d'utilisation, nous retrouvons des bornes de déviations pour le problème du rangement de boîtes (bin-packing problem)." @default.
• W1979732034 created "2016-06-24" @default.
• W1979732034 creator A5059555567 @default.
• W1979732034 date "2007-05-01" @default.
• W1979732034 modified "2023-10-15" @default.
• W1979732034 title "Infimum-convolution description of concentration properties of product probability measures, with applications" @default.
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• W1979732034 doi "https://doi.org/10.1016/j.anihpb.2006.05.003" @default.
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