High dimensional random sections of isotropic convex bodies Academic Article uri icon


  • We study two properties of random high dimensional sections of convex bodies. In the first part of the paper we estimate the central section function | K F |n - k1 / k for random F Gn, k and K Rn a centrally symmetric isotropic convex body. This partially answers a question raised by V.D. Milman and A. Pajor (see [V.D. Milman, A. Pajor, Isotropic positions and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, in: Lecture Notes in Math., vol. 1376, Springer, 1989, p. 88]). In the second part we show that every symmetric convex body has random high dimensional sections F Gn, k with outer volume ratio bounded byovr (K F) C frac(n, n - k) log (1 + frac(n, n - k)) . 2009 Elsevier Inc. All rights reserved.

published proceedings


author list (cited authors)

  • Alonso-Gutierrez, D., Bastero, J., Bernues, J., & Paouris, G.

citation count

  • 0

complete list of authors

  • Alonso-Gutierrez, David||Bastero, Jesus||Bernues, Julio||Paouris, Grigoris

publication date

  • January 2010