Abstract
Let µ = µ 1 ⊗ … ⊗ µ n denote a product probability measure on ℝn with compact support. We present a simple proof to get concentration results for convex functions on ℝn under µ. We use the infimum convex convolution description of the concentration phenomenon introduced by Maurey [14]. The main result of this paper is a transportation inequality for the measure µ comparable to the classical transportation inequality for the canonical Gaussian measure on ℝn. In application, we present Khinchine Kahane inequalities for norms of random series with non-symmetric Bernoulli coefficients.
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Samson, PM. (2003). Concentration Inequalities for Convex Functions on Product Spaces. In: Giné, E., Houdré, C., Nualart, D. (eds) Stochastic Inequalities and Applications. Progress in Probability, vol 56. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8069-5_4
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DOI: https://doi.org/10.1007/978-3-0348-8069-5_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9428-9
Online ISBN: 978-3-0348-8069-5
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