A tight lower bound on the minimal dispersion
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913274179616768 |
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| author | Trödler, Matěj Volec, Jan Vybíral, Jan |
| author_facet | Trödler, Matěj Volec, Jan Vybíral, Jan |
| contents | We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very small class of test boxes, which allows us to reduce bounding the dispersion to a problem in extremal set theory. Specifically, we translate a lower bound on the size of $r$-cover-free families to a lower bound on the inverse of the minimal dispersion of a point set. The lower bound we obtain matches the recently obtained upper bound on the minimal dispersion up to logarithmic terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10666 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A tight lower bound on the minimal dispersion Trödler, Matěj Volec, Jan Vybíral, Jan Numerical Analysis We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very small class of test boxes, which allows us to reduce bounding the dispersion to a problem in extremal set theory. Specifically, we translate a lower bound on the size of $r$-cover-free families to a lower bound on the inverse of the minimal dispersion of a point set. The lower bound we obtain matches the recently obtained upper bound on the minimal dispersion up to logarithmic terms. |
| title | A tight lower bound on the minimal dispersion |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2311.10666 |