WEIGHTED POINCARE-TYPE INEQUALITIES FOR CAUCHY AND OTHER CONVEX MEASURES

• 成果类型: Article
• 署名作者: Bobkov, Sergey G.; Ledoux, Michel
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP407
• 发表日期: 2009
• 页码: 403-427
• 关键词: logarithmic sobolev inequalities; brunn-minkowski inequality; analytic inequalities; PROBABILITY-MEASURES; diffusion

摘要

Brascamp-Lieb-type, weighted Poincare-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general kappa-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.