Isoperimetry for spherically symmetric log-concave probability measures

Rev. Mat. Iberoamericana, Tome 27 (2011) no. 1, p. 93-122 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2011-01-15
Classification:  isoperimetric inequalities,  log-concave measures,  26D10,  60E15,  28A75