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Asymptotic properties of two affine invariants for 1-unconditional convex bodies |
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| Authors: | XIE Fu-sheng HE Bin-wu YI Jun |
| Institution: | 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China;Basic Education Department, Tianhua College of Shanghai Normal University, Shanghai 201815, P. R. China 2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
| Abstract: | Let K be a 1-unconditional convex bodies in Euclidean spaces. We study the asymptotic properties of two affine invariants m2(K) and S2(K) for a random simplex inside K. As an application, we discuss the asymptotic properties of two affine invariants m2(Bnp) and S2(Bnp), where Bnp = {χ∈ Rn: ‖χ‖p ≤ 1}. |
| Keywords: | convex body 1-unconditional convex body isotropic constant Sylvester's problem random simplex |
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