Isoperimetric and analytic inequalities for log-concave probability measures

• 成果类型: Article
• 署名作者: Bobkov, SG
• 署名单位: Syktyvkar State University; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022677553
• 发表日期: 1999
• 页码: 1903-1921
• 关键词: logarithmic sobolev inequalities; convex-bodies; exponential integrability; brunn-minkowski; SPACES; bounds

摘要

We discuss an approach, based on the Brunn-Minkowski inequality, to isoperimetric and analytic inequalities for probability measures on Euclidean space with logarithmically concave densities. In particular, we show that such measures have positive isoperimetric constants in the sense of Cheeger and thus always share Poincare-type inequalities. We then describe those log-concave measures which satisfy isoperimetric inequalities of Gaussian type. The results are precised in dimension 1.