Weighted Poincaré-type Inequalities for Cauchy and Other Convex Measures1 by Sergey

نویسندگان

  • G. BOBKOV
  • MICHEL LEDOUX
  • M. LEDOUX
چکیده

Brascamp–Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general κ-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 weight in the class of concave probability measures under consideration.

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Weighted Poincaré-type Inequalities for Cauchy and Other Convex Measures

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تاریخ انتشار 2009