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Volume thresholds for Gaussian and spherical random polytopes and their duals

Volume thresholds for Gaussian and spherical random polytopes and their duals

Let $g$ be a Gaussian random vector in $\mathbb{R}^n$. Let $N=N(n)$ be a positive integer and let $K_N$ be the convex hull of $N$ independent copies of $g$. Fix $R>0$ and consider the ratio of volumes $V_N:={\mathbb E}\mathop{\rm vol}(K_N\cap RB_2^n)/\!\