Weighted Poincaré-type inequalities for Cauchy and other convex measures

Bobkov, Sergey G.; Ledoux, Michel

Ann. Probab., Tome 37 (2009) no. 1, p. 403-427 / Harvested from Project Euclid

Résumé

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.

Publié le : 2009-03-15
Classification: Brascamp–Lieb-type inequalities, weighted Poincaré-type inequalities, logarithmic Sovolev inequalities, infimum convolution, measure concentration, Cheeger-type inequalities, 46G12, 60B11, 60G07

@article{1241099916,
     author = {Bobkov, Sergey G. and Ledoux, Michel},
     title = {Weighted Poincar\'e-type inequalities for Cauchy and other convex measures},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 403-427},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1241099916}
}

Bobkov, Sergey G.; Ledoux, Michel. Weighted Poincaré-type inequalities for Cauchy and other convex measures. Ann. Probab., Tome 37 (2009) no. 1, pp.  403-427. http://gdmltest.u-ga.fr/item/1241099916/