Weighted Poincaré-type inequalities for Cauchy and other convex measures
Authors:
- Sergey G. BobkovSBSergey G. Bobkov
- Michel LedouxMLMichel Ledoux
Open Access
- 1 March 2009
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 37 (2) , 403-427
Abstract
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. Cheeger-type isoperimetric inequalities are investigated similarly, giving rise to a common weight in the class of concave probability measures under consideration.Keywords
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