JournalsrmiVol. 27, No. 1pp. 93–122

Isoperimetry for spherically symmetric log-concave probability measures

  • Nolwen Huet

    Université de Toulouse, France
Isoperimetry for spherically symmetric log-concave probability measures cover
Download PDF

Abstract

We prove an isoperimetric inequality for probability measures μ\mu on Rn\mathbb{R}^n with density proportional to exp(ϕ(λx))\exp(-\phi(\lambda |x|)), where x|x| is the euclidean norm on Rn\mathbb{R}^n and ϕ\phi is a non-decreasing convex function. It applies in particular when ϕ(x)=xα\phi(x)=x^\alpha with α1\alpha \ge 1. Under mild assumptions on ϕ\phi, the inequality is dimension-free if λ\lambda is chosen such that the covariance of μ\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