The Annals of Probability

Weighted Poincaré-type inequalities for Cauchy and other convex measures

Sergey G. Bobkov and Michel Ledoux

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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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Ann. Probab., Volume 37, Number 2 (2009), 403-427.

First available in Project Euclid: 30 April 2009

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Zentralblatt MATH identifier

Primary: 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12] 60B11: Probability theory on linear topological spaces [See also 28C20] 60G07: General theory of processes

Brascamp–Lieb-type inequalities weighted Poincaré-type inequalities logarithmic Sovolev inequalities infimum convolution measure concentration Cheeger-type inequalities


Bobkov, Sergey G.; Ledoux, Michel. Weighted Poincaré-type inequalities for Cauchy and other convex measures. Ann. Probab. 37 (2009), no. 2, 403--427. doi:10.1214/08-AOP407.

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