Point sets with optimal order of extreme and periodic discrepancy. (English) Zbl 1503.11107
This paper is a continuation and extension of [A. Hinrichs et al., Acta Arith. 199, No. 2, 163–198 (2021; Zbl 1483.11158)]. The notion of discrepancy is a quantitative measure for the regularity of the distribution of a point configuration in the multidimensional unit cube. Choosing different classes of test sets leads to different notions of discrepancy.
In this paper, the authors study \(L^p\) discrepancies with respect to a) axis-parallel boxes anchored at the origin, b) all axis-parallel boxes, c) axis-parallel boxes which are allowed to “wrap around” on the torus.
These classes of test sets lead to the notions of a) star discrepancy, b) extremal discrepancy, and c) periodic discrepancy. The authors are interested in the relation between these different notions of discrepancy, and in their respective minimal possible asymptotic order.
In this paper, the authors study \(L^p\) discrepancies with respect to a) axis-parallel boxes anchored at the origin, b) all axis-parallel boxes, c) axis-parallel boxes which are allowed to “wrap around” on the torus.
These classes of test sets lead to the notions of a) star discrepancy, b) extremal discrepancy, and c) periodic discrepancy. The authors are interested in the relation between these different notions of discrepancy, and in their respective minimal possible asymptotic order.
Reviewer: Christoph Aistleitner (Graz)
MSC:
| 11K38 | Irregularities of distribution, discrepancy |
Citations:
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