Location of Repository

Volume of the polar of random sets and shadow systems

By Dario Cordero-Erausquin, Matthieu Fradelizi, Grigoris Paouris and Peter Pivovarov


International audienceWe 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 Blaschke–Santaló 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

Topics: [ MATH ] Mathematics [math]
Publisher: Springer Verlag
Year: 2014
DOI identifier: 10.1007/s00208-014-1156-x
OAI identifier: oai:HAL:hal-01122831v1
Provided by: Hal-Diderot
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • https://hal.sorbonne-universit... (external link)
  • https://hal.sorbonne-universit... (external link)
  • https://hal.sorbonne-universit... (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.