Hidden low-discrepancy structures in random point sets
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915803161427968 |
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| author | Suzuki, Kohei Goda, Takashi |
| author_facet | Suzuki, Kohei Goda, Takashi |
| contents | We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the number of geometric patterns for $(0, m, d)$-nets in base $b$. By applying the elementary probability bounds together with this counting result, we then give scaling conditions on $N$ as a function of $m$ such that this probability converges to $1$ and $0$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hidden low-discrepancy structures in random point sets Suzuki, Kohei Goda, Takashi Combinatorics We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the number of geometric patterns for $(0, m, d)$-nets in base $b$. By applying the elementary probability bounds together with this counting result, we then give scaling conditions on $N$ as a function of $m$ such that this probability converges to $1$ and $0$, respectively. |
| title | Hidden low-discrepancy structures in random point sets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.15007 |