Sharpening work of the first two authors, for every proportion λ ∈ (0, 1) we provide exact quantitative relations between global parameters of n-dimensional symmetric convex bodies and the diameter of their random ⌊λn⌋-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.
Giannopoulos, A., Milman, V. D., & Tsolomitis, A. (2005). Asymptotic formulas for the diameter of sections of symmetric convex bodies. Journal of Functional Analysis, 223(1), 86–108. https://doi.org/10.1016/j.jfa.2004.10.006