On the volume of caps and bounding the mean-width of an isotropic convex body

• Autores: Peter Pivovarov
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 149, Nº 2, 2010, págs. 317-331
• Idioma: inglés
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• Resumen

  • Let K be a convex body which is (i) symmetric with respect to each of the coordinate hyperplanes and (ii) in isotropic position. We prove that most linear functionals acting on K exhibit super-Gaussian tail behavior. Using known facts about the mean-width of such bodies, we then deduce strong lower bounds for the volume of certain caps. We also prove a converse statement. Namely, if an arbitrary isotropic convex body (not necessarily satisfying (i)) exhibits similar cap-behavior, then one can bound its mean-width.