We prove an isoperimetric inequality for probability measures on with density proportional to , where is the euclidean norm on and is a non-decreasing convex function. It applies in particular when with . Under mild assumptions on , the inequality is dimension-free if is chosen such that the covariance of is the identity.
Cite this article
Nolwen Huet, Isoperimetry for spherically symmetric log-concave probability measures. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 93–122DOI 10.4171/RMI/631