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- W2963552331 abstract "Let $K$ be a convex body in $mathbb{R} ^n$ and $f : partial K rightarrow mathbb{R} _+$ a continuous, strictly positive function with $int limits _{partial K} f(x) mathrm{d} mu _{partial K}(x) = 1$. We give an upper bound for the approximation of $K$ in the symmetric difference metric by an arbitrarily positioned polytope $P_f$ in $mathbb{R} ^n$ having a fixed number of vertices. This generalizes a result by Ludwig, Schütt and Werner [36]. The polytope $P_f$ is obtained by a random construction via a probability measure with density $f$. In our result, the dependence on the number of vertices is optimal. With the optimal density $f$, the dependence on $K$ in our result is also optimal." @default.
- W2963552331 created "2019-07-30" @default.
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- W2963552331 date "2018-01-01" @default.
- W2963552331 modified "2023-10-02" @default.
- W2963552331 title "Approximation of smooth convex bodies by random polytopes" @default.
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- W2963552331 doi "https://doi.org/10.1214/17-ejp131" @default.
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