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. \"Osterreich. 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 $\varepsilon$.

翻译：我们证明最低球面分布的上限和下限是最低球面分布值的上限和下限,比Rote 和 Tichy 先前的估算值有所改善,[对曲线多边形近似应用的球面分布,Anz. \ "Osterreich. Akad. Wiss. Math.-Natur. Kl. 132(1995), 3-10]。特别是,我们看到最低球面分布值的逆值(n(\ varepsilon, d)美元是固定的 $\varepsilon>0美元,在环境空间的维度上线性值为$d.。我们还从预期的分布线上得出了独立和统一地随机从Euclide 单位球区选择的点的上上方和下方界限。就相应的逆值 $@lepsilde{N}(\ varepsilon, d) 而言,我们的界限最符合对美元的依赖度。