Volume of the polar of random sets and shadow systems Academic Article uri icon

abstract

  • 2014, Springer-Verlag Berlin Heidelberg. We obtain optimal inequalities for the volume of the polar of random sets, generated for instance by the convex hull of independent random vectors in Euclidean space. Extremizers are given by random vectors uniformly distributed in Euclidean balls. This provides a random extension of the BlaschkeSantal inequality which, in turn, can be derived by the law of large numbers. The method involves shadow systems, their connection to Busemann type inequalities, and how they interact with functional rearrangement inequalities.

published proceedings

  • MATHEMATISCHE ANNALEN

author list (cited authors)

  • Cordero-Erausquin, D., Fradelizi, M., Paouris, G., & Pivovarov, P.

citation count

  • 13

complete list of authors

  • Cordero-Erausquin, Dario||Fradelizi, Matthieu||Paouris, Grigoris||Pivovarov, Peter

publication date

  • August 2015