Abstract
Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and combinatorial optimization, and studies its theoretical properties. Our result solves both the exact optimal spherical point configurations in certain cases and the minimal energy asymptotics under general assumptions. Connections between our results and the L1-principal component analysis and quasi-Monte Carlo methods are also discussed.
| Original language | American English |
|---|---|
| Pages (from-to) | 131-154 |
| Number of pages | 24 |
| Journal | Random Structures and Algorithms |
| Volume | 62 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2023 |
ASJC Scopus subject areas
- Software
- General Mathematics
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
Keywords
- discrepancy
- minimal energy
- minimax spherical design