Weighted poincaré-type inequalities for cauchy and other convex measures

Sergey G. Bobkov, Michel Ledoux

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

Brascamp-Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general ?-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinite-dimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of this family of measures. Cheegertype isoperimetric inequalities are investigated similarly, giving rise to a common eight in the class of concave probability measures under consideration.

Original languageEnglish (US)
Pages (from-to)403-427
Number of pages25
JournalAnnals of Probability
Volume37
Issue number2
DOIs
StatePublished - Mar 2009

Keywords

  • Brascamp-Lieb-type inequalities
  • Cheeger-type inequalities
  • Infimum convolution
  • Iogarithmic Sovolev inequalities
  • Measure concentration
  • Weighted Poincaré-type inequalities

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