2021/03/22 by Joscha Prochno, Prochno, Joscha, Daniel Rudolf +1 · 1 citation
Mathematics · #11K38 #51F99 #68U05 #FOS: Mathematics #Geometry and complex manifolds #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Numerical Analysis (math.NA) #Point processes and geometric inequalities #Primary 60D05 #Secondary 03D15
paper · pdf · doi:10.48550/arxiv.2103.11701
openalex publication_date 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(ε,d) of the minimal spherical dispersion is, for fixed ε>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 \widetildeN(ε,d), our bounds are optimal with respect to the dependence on ε.