最小球面色散
The minimal spherical dispersion
摘要：
我们证明了上界和下界的最小球形色散，改善以前的估计获得的罗特和Tichy [球形色散与应用程序的曲线，Anz的折线逼近。奥地利阿卡德聪明数学自然。KL. 132（1995），3- 10]。特别地，我们看到，对于固定的$\varepsilon>0$，最小球面色散的逆$N(\varepsilon,d)$在周围空间的维度$d$中是线性的。我们还推导出上，下界的预期分散的点，独立和均匀随机从欧几里德单位球。在相应的逆$\widetilde{N}(\varepsilon,d)$方面，我们的界限是最佳的依赖于$\varepsilon$。
英文摘要：
We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy [Spherical dispersion with an application to polygonal approximation of curves, Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 132 (1995), 3--10]. In particular, we see that the inverse $N(\varepsilon,d)$ of the minimal spherical dispersion is, for fixed $\varepsilon>0$, linear in the dimension $d$ of the ambient space. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere. In terms of the corresponding inverse $\widetilde{N}(\varepsilon,d)$, our bounds are optimal with respect to the dependence on $\varepsilon$.
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