A probabilistic take on isoperimetric-type inequalities

作者：Paouris Grigoris; Pivovarov Peter^*

来源：Advances in Mathematics, 2012, 230(3): 1402-1422.

DOI：10.1016/j.aim.2012.03.019

• Isoperimetric inequalities
• Rearrangements
• Random convex sets

We extend a theorem of Groemer on the expected volume of a random polytope in a convex body. The extension involves various ways of generating random convex sets. We also treat the case of absolutely continuous probability measures rather than convex bodies. As an application, we obtain a new proof of a recent result due to Lutwak, Yang and Zhang on the volume of Orlicz-centroid bodies.

• 出版日期2012-6-20