In this paper we prove upper and lower bounds on the minimal spherical dispersion. In particular, we see that the inverse $N(\varepsilon,d)$ of the minimal spherical dispersion is, for fixed $\varepsilon>0$, up to logarithmic terms linear in the dimension $d$. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere.
翻译:在本文中,我们证明了最小球体分布的上下界限。特别是,我们看到最小球体分布的逆值$N(\ varepsilon, d)是固定的$N(\ varepsilon, d) $0, 最高为维的对数线线性值 $d$。我们还从单球体范围内独立、统一随机选择的点的预期分布线上得出上下界限。