Isoperimetry for spherically symmetric log-concave probability measures

Details Isoperimetry for spherically symmetric log-concave probability measures Isoperimetry for spherically symmetric log-concave probability measures

2009-02-04

arxiv.org/abs/0902.0743v2

Mathematics

Probability

Scientific paper

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 $\alpha\ge1$. 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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