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• W1970385778 abstract "Let $$X_1,ldots ,X_N$$ be independent random vectors uniformly distributed on an isotropic convex body $$Ksubset mathbb {R}^n$$ , and let $$K_N$$ be the symmetric convex hull of $$X_i$$ ’s. We show that with high probability $$ L_{K_N}le C sqrt{log (2N/n)}$$ , where $$C$$ is an absolute constant. This result closes the gap in known estimates in the range $$Cnle Nle n^{1+delta }$$ . Furthermore, we extend our estimates to the symmetric convex hulls of vectors $$y_1 X_1, dots , y_N X_N$$ , where $$y=(y_1, dots , y_N)$$ is a vector in $$mathbb {R}^N$$ . Finally, we discuss the case of a random vector $$y$$ ." @default.
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• W1970385778 date "2015-01-27" @default.
• W1970385778 modified "2023-10-05" @default.
• W1970385778 title "On the Isotropic Constant of Random Polytopes" @default.
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• W1970385778 doi "https://doi.org/10.1007/s12220-015-9567-9" @default.
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