Weighted Poincaré-type inequalities for Cauchy and other convex measures
Authors:
- Sergey G. BobkovSBSergey G. Bobkov
- Michel LedouxMLMichel Ledoux
Preprint
Abstract
Brascamp--Lieb-type, weighted Poincar\'{e}-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general $\kappa$-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. Cheeger-type isoperimetric inequalities are investigated similarly, giving rise to a common weight in the class of concave probability measures under consideration.Keywords
All Related Versions
- Version 1, 2009-06-09, ArXiv
- Published version: The Annals of Probability, 37 (2), 403.
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