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- W4289763005 abstract "For an isotropic convex body $Ksubsetmathbb{R}^n$ we consider the isotropic constant $L_{K_N}$ of the symmetric random polytope $K_N$ generated by $N$ independent random points which are distributed according to the cone probability measure on the boundary of $K$. We show that with overwhelming probability $L_{K_N}leq Csqrt{log(2N/n)}$, where $Cin(0,infty)$ is an absolute constant. If $K$ is unconditional we argue that even $L_{K_N}leq C$ with overwhelming probability. The proofs are based on concentration inequalities for sums of sub-exponential or sub-Gaussian random variables, respectively, and, in the unconditional case, on a new $psi_2$-estimate for linear functionals with respect to the cone measure in the spirit of Bobkov and Nazarov, which might be of independent interest." @default.
- W4289763005 created "2022-08-04" @default.
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- W4289763005 date "2018-07-06" @default.
- W4289763005 modified "2023-09-30" @default.
- W4289763005 title "The isotropic constant of random polytopes with vertices on convex surfaces" @default.
- W4289763005 doi "https://doi.org/10.48550/arxiv.1807.02396" @default.
- W4289763005 hasPublicationYear "2018" @default.
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