Details

Autor(en) / Beteiligte

• Prochno, Joscha
• Rudolf, Daniel

Titel

The Minimal Spherical Dispersion

Ist Teil von

• The Journal of geometric analysis, 2024, Vol.34 (3), p.85-85, Article 85

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2024

Link zum Volltext

Quelle

SpringerLink (Online service)

Beschreibungen/Notizen

• We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy in (Anz Österreich Akad Wiss Math Nat Kl 132:3–10, 1995). 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 N ~ ( ε , d ) , our bounds are optimal with respect to the dependence on ε .