Minimal Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913631993593856 |
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| author | Etayo, Ujué López-Gómez, Pedro R. |
| author_facet | Etayo, Ujué López-Gómez, Pedro R. |
| contents | We study the Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ of $2$-dimensional subspaces of $\mathbb{R}^4$. We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform measure, and we obtain asymptotic upper and lower bounds for the minimal discrete energies, with matching orders for the next-order terms. Additionally, we define a determinantal point process on $\operatorname{Gr}_{2,4}$ and compute the expected energy of the points coming from this random process, thereby obtaining explicit constants in the upper bounds for the Riesz and logarithmic energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ Etayo, Ujué López-Gómez, Pedro R. Classical Analysis and ODEs Probability 31C12, 60G55 (Primary) 33C50, 41A60, 42C10 (Secondary) We study the Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ of $2$-dimensional subspaces of $\mathbb{R}^4$. We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform measure, and we obtain asymptotic upper and lower bounds for the minimal discrete energies, with matching orders for the next-order terms. Additionally, we define a determinantal point process on $\operatorname{Gr}_{2,4}$ and compute the expected energy of the points coming from this random process, thereby obtaining explicit constants in the upper bounds for the Riesz and logarithmic energies. |
| title | Minimal Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ |
| topic | Classical Analysis and ODEs Probability 31C12, 60G55 (Primary) 33C50, 41A60, 42C10 (Secondary) |
| url | https://arxiv.org/abs/2501.00424 |