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Asymptotic formulas for the diameter of sections of symmetric convex bodies |
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| Authors: | Apostolos Giannopoulos Vitali D Milman Antonis Tsolomitis |
| Institution: | a Department of Mathematics, University of Crete, Heraklion, Greece b Department of Mathematics, Tel Aviv University, Tel Aviv, Israel c Department of Mathematics, University of the Aegean, Karlovassi, Greece |
| Abstract: | 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. |
| Keywords: | primary 46B07 secondary 52A20 52A40 |
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