# Isoperimetry for spherically symmetric log-concave probability measures

### Nolwen Huet

Université de Toulouse, France

## Abstract

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.

## Cite this article

Nolwen Huet, Isoperimetry for spherically symmetric log-concave probability measures. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 93–122

DOI 10.4171/RMI/631