Revista Matemática Iberoamericana

Isoperimetry for spherically symmetric log-concave probability measures

Nolwen Huet

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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.

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Rev. Mat. Iberoamericana, Volume 27, Number 1 (2011), 93-122.

First available in Project Euclid: 4 February 2011

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Primary: 26D10: Inequalities involving derivatives and differential and integral operators 60E15: Inequalities; stochastic orderings 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

isoperimetric inequalities log-concave measures


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

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