Discrepancy of determinantal point processes on compact, connected two-point homogeneous spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910245665636352 |
|---|---|
| author | Beltrán, Carlos Etayo, Ujué Gigante, Giacomo López-Gómez, Pedro R. Matzke, Ryan W. |
| author_facet | Beltrán, Carlos Etayo, Ujué Gigante, Giacomo López-Gómez, Pedro R. Matzke, Ryan W. |
| contents | We study the $L^{\infty}$ discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective spaces. Using concentration inequalities and variance estimates for the number of points in metric balls, we derive general upper bounds for the discrepancy of homogeneous determinantal point processes. In the particular case of the harmonic ensemble, we show that the discrepancy of $N$ points is $O((N^{1-1/D})^{1/2}\log N)$ with high probability, where $D$ denotes the real dimension of the manifold. For the projective ensemble on $\mathbb{CP}^d$, we obtain the sharper bound $O((N^{1-1/D}\log N)^{1/2})$. These results extend previously known discrepancy estimates for determinantal point processes on the sphere to all compact, connected two-point homogeneous spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrepancy of determinantal point processes on compact, connected two-point homogeneous spaces Beltrán, Carlos Etayo, Ujué Gigante, Giacomo López-Gómez, Pedro R. Matzke, Ryan W. Classical Analysis and ODEs Probability 11K38, 60G55 We study the $L^{\infty}$ discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective spaces. Using concentration inequalities and variance estimates for the number of points in metric balls, we derive general upper bounds for the discrepancy of homogeneous determinantal point processes. In the particular case of the harmonic ensemble, we show that the discrepancy of $N$ points is $O((N^{1-1/D})^{1/2}\log N)$ with high probability, where $D$ denotes the real dimension of the manifold. For the projective ensemble on $\mathbb{CP}^d$, we obtain the sharper bound $O((N^{1-1/D}\log N)^{1/2})$. These results extend previously known discrepancy estimates for determinantal point processes on the sphere to all compact, connected two-point homogeneous spaces. |
| title | Discrepancy of determinantal point processes on compact, connected two-point homogeneous spaces |
| topic | Classical Analysis and ODEs Probability 11K38, 60G55 |
| url | https://arxiv.org/abs/2605.22295 |