On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities

DOI10.1214/08-AIHP309zbMath1204.60025arXiv0805.0987MaRDI QIDQ974769

Florent Malrieu, Djalil Chafaï

Publication date: 7 June 2010

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.0987

zbMATH Keywords

functional inequalitiesconcentration of measuremixtures of distributionsPoincaré inequalitiesGaussian boundsmass transportationdeviation inequalitiestransportation of measureband isoperimetryfinite Gaussian mixturesGross logarithmic Sobolev inequalitiesMallows or Wasserstein distancetails probabilitiestransportation cost distances

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational problems in a geometric measure-theoretic setting (49Q20) Statistical distribution theory (62E99)

Related Items (8)

Some recent developments in functional inequalities ⋮ Bounds on the Poincaré constant for convolution measures ⋮ Stein's density method for multivariate continuous distributions ⋮ Convergence rate for geometric statistics of point processes having fast decay of dependence ⋮ Transportation inequalities: from Poisson to Gibbs measures ⋮ On the convex Poincaré inequality and weak transportation inequalities ⋮ Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape ⋮ Dimension-free log-Sobolev inequalities for mixture distributions

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