A New Construction of Forests with Low Visibility
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915064763645952 |
|---|---|
| author | Kashkan, Kirill |
| author_facet | Kashkan, Kirill |
| contents | A set of points with finite density is constructed in $\mathbb{R}^d$, with $d\geq2$, by adding points to a Poisson process such that any line segment of length $O\left(\varepsilon^{-(d-1)}\ln\varepsilon^{-1}\right)$ in $\mathbb{R}^d$ will contain one of the points of the set within distance $\varepsilon$ of it. The constant implied by the big-$O$ notation depends on the dimension only. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A New Construction of Forests with Low Visibility Kashkan, Kirill Metric Geometry Combinatorics Probability A set of points with finite density is constructed in $\mathbb{R}^d$, with $d\geq2$, by adding points to a Poisson process such that any line segment of length $O\left(\varepsilon^{-(d-1)}\ln\varepsilon^{-1}\right)$ in $\mathbb{R}^d$ will contain one of the points of the set within distance $\varepsilon$ of it. The constant implied by the big-$O$ notation depends on the dimension only. |
| title | A New Construction of Forests with Low Visibility |
| topic | Metric Geometry Combinatorics Probability |
| url | https://arxiv.org/abs/2407.01633 |