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- W2952345851 abstract "Let K be a convex body in $R^d$. A random polytope is the convex hull $[x_1,...,x_n]$ of finitely many points chosen at random in K. $Bbb E(K,n)$ is the expectation of the volume of a random polytope of n randomly chosen points. I. B'ar'any showed that we have for convex bodies with $C^3$ boundary and everywhere positive curvature $$ c(d)lim_{n to infty} frac {vol_d(K)-Bbb E(K,n)}{(frac{vol_d(K)}{n})^{frac{2}{d+1}}} =int_{partial K} kappa(x)^{frac{1}{d+1}}dmu(x) $$ where $kappa(x)$ denotes the Gauss-Kronecker curvature. We show that the same formula holds for all convex bodies if $kappa(x)$ denotes the generalized Gauss-Kronecker curvature." @default.
- W2952345851 created "2019-06-27" @default.
- W2952345851 creator A5046396053 @default.
- W2952345851 date "1993-02-04" @default.
- W2952345851 modified "2023-09-27" @default.
- W2952345851 title "Random polytopes and affine surface area" @default.
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