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arXiv · 0906.1651

Weighted Poincaré-type inequalities for Cauchy and other convex measures

Sergey G. Bobkov·Michel Ledoux
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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.

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Sergey G. Bobkov, Michel Ledoux. 2009-06-09. Weighted Poincaré-type inequalities for Cauchy and other convex measures. https://doi.org/10.1214/08-aop407

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