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October 1999 Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures
S. G. Bobkov
Ann. Probab. 27(4): 1903-1921 (October 1999). DOI: 10.1214/aop/1022874820

Abstract

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.

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S. G. Bobkov. "Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures." Ann. Probab. 27 (4) 1903 - 1921, October 1999. https://doi.org/10.1214/aop/1022874820

Information

Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0964.60013
MathSciNet: MR1742893
Digital Object Identifier: 10.1214/aop/1022874820

Subjects:
Primary: 60J75
Secondary: 05A18, 60G09, 60G57

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • October 1999
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