Open Access
January, 2011 Isoperimetry for spherically symmetric log-concave probability measures
Nolwen Huet
Rev. Mat. Iberoamericana 27(1): 93-122 (January, 2011).


We prove an isoperimetric inequality for probability measures $\mu$ on $\mathbb{R}^n$ with density proportional to $\exp(-\phi(\lambda |x|))$, where $|x|$ is the euclidean norm on $\mathbb{R}^n$ and $\phi$ is a non-decreasing convex function. It applies in particular when $\phi(x)=x^\alpha$ with $\alpha \ge 1$. Under mild assumptions on $\phi$, the inequality is dimension-free if $\lambda$ is chosen such that the covariance of $\mu$ is the identity.


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Nolwen Huet . "Isoperimetry for spherically symmetric log-concave probability measures." Rev. Mat. Iberoamericana 27 (1) 93 - 122, January, 2011.


Published: January, 2011
First available in Project Euclid: 4 February 2011

zbMATH: 1225.26035
MathSciNet: MR2815733

Primary: 26D10 , 28A75 , 60E15

Keywords: Isoperimetric inequalities , Log-concave measures

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 1 • January, 2011
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