On the expected L2-discrepancy of stratified samples from parallel lines

Fuente: arXiv
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Autor principal: Pausinger, Florian
Formato: Preprint
Publicado: 2023
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author Pausinger, Florian
author_facet Pausinger, Florian
contents We study the expected $\mathcal{L}_2$-discrepancy of stratified samples generated from special equi-volume partitions of the unit square. The partitions are defined via parallel lines that are all orthogonal to the diagonal of the square. It is shown that the expected discrepancy of stratified samples derived from these partitions is a factor 2 smaller than the expected discrepancy of the same number of i.i.d uniformly distributed random points in the unit square. We conjecture that this is best possible among all partitions generated from parallel lines.
format Preprint
id arxiv_https___arxiv_org_abs_2310_13927
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the expected L2-discrepancy of stratified samples from parallel lines
Pausinger, Florian
Number Theory
11K38, 05A18, 60C05,
We study the expected $\mathcal{L}_2$-discrepancy of stratified samples generated from special equi-volume partitions of the unit square. The partitions are defined via parallel lines that are all orthogonal to the diagonal of the square. It is shown that the expected discrepancy of stratified samples derived from these partitions is a factor 2 smaller than the expected discrepancy of the same number of i.i.d uniformly distributed random points in the unit square. We conjecture that this is best possible among all partitions generated from parallel lines.
title On the expected L2-discrepancy of stratified samples from parallel lines
topic Number Theory
11K38, 05A18, 60C05,
url https://arxiv.org/abs/2310.13927