Open Access
March 2009 Weighted Poincaré-type inequalities for Cauchy and other convex measures
Sergey G. Bobkov, Michel Ledoux
Ann. Probab. 37(2): 403-427 (March 2009). DOI: 10.1214/08-AOP407


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.


Download Citation

Sergey G. Bobkov. Michel Ledoux. "Weighted Poincaré-type inequalities for Cauchy and other convex measures." Ann. Probab. 37 (2) 403 - 427, March 2009.


Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1178.46041
MathSciNet: MR2510011
Digital Object Identifier: 10.1214/08-AOP407

Primary: ‎46G12 , 60B11 , 60G07

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

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • March 2009
Back to Top