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Weighted Poincaré-Type Inequalities for Cauchy and Other Convex Measures
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Weighted Poincaré-Type Inequalities for Cauchy and Other Convex Measures
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Journal Article
Weighted Poincaré-Type Inequalities for Cauchy and Other Convex Measures
2009
Overview
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.
Publisher
Institute of Mathematical Statistics,The Institute of Mathematical Statistics
Subject
/ 60B11
/ 60G07
/ Brascamp–Lieb-type inequalities
/ Density
/ Exact sciences and technology
/ logarithmic Sovolev inequalities
/ Modeling
/ Probability theory and stochastic processes
/ Probability theory on algebraic and topological structures
/ Sciences and techniques of general use
/ Studies
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