Abstract
Brascamp-Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general ?-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. Cheegertype isoperimetric inequalities are investigated similarly, giving rise to a common eight in the class of concave probability measures under consideration.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 403-427 |
| Number of pages | 25 |
| Journal | Annals of Probability |
| Volume | 37 |
| Issue number | 2 |
| DOIs | |
| State | Published - Mar 2009 |
Keywords
- Brascamp-Lieb-type inequalities
- Cheeger-type inequalities
- Infimum convolution
- Iogarithmic Sovolev inequalities
- Measure concentration
- Weighted Poincaré-type inequalities
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