Asymptotic formulas for the diameter of sections of symmetric convex bodies

Sharpening work of the first two authors, for every proportion ∈ (0, 1) we provide exact quantitative relations between global parameters of n-dimensional symmetric convex bodies and the diameter of their random n -dimensional sections. Using recent results of Gromov and Vershynin, we obtain an “asymptotic formula” for the diameter of random proportional sections. © 2004 Elsevier Inc. All rights reserved.