Isoperimetry for spherically symmetric log-concave probability measures

Nolwen Huet (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Probabilités [math.PR]

Nolwen Huet. Isoperimetry for spherically symmetric log-concave probability measures. 2009. ⟨hal-00358888v2⟩