The Annals of Probability
- Ann. Probab.
- Volume 27, Number 4 (1999), 1903-1921.
Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures
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 Poincaré-type inequalities. We then describe those log-concave measures which satisfy isoperimetric inequalities of Gaussian type. The results are precised in dimension 1.
Ann. Probab. Volume 27, Number 4 (1999), 1903-1921.
First available in Project Euclid: 31 May 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Exchangeable random partition ranked frequencies random discrete distribution two-parameter Poisson –Dirichlet stable subordinator coagulation,fragmentation time reversal Ewens sampling formula
Bobkov, S. G. Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures. Ann. Probab. 27 (1999), no. 4, 1903--1921. doi:10.1214/aop/1022874820. http://projecteuclid.org/euclid.aop/1022874820.