Isoperimetric and analytic inequalities for log-concave probability measures

被引:158
作者
Bobkov, SG [1 ]
机构
[1] Syktyvkar State Univ, Dept Math, Syktyvkar 167001, Russia
[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
关键词
logarithmically concave measures; isoperimetric inequalities; Poincare-type inequalities; logarithmic Sobolev inequalities; isoperimetric constants;
D O I
10.1214/aop/1022677553
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];
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.
引用
收藏
页码:1903 / 1921
页数:19
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