Limits of Discrete Energy of Families of Increasing Sets
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908646266372096 |
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| author | Nathan, Hari Sarang |
| author_facet | Nathan, Hari Sarang |
| contents | The Hausdorff dimension of a set can be detected using the Riesz energy. Here, we consider situations where a sequence of points, $\{x_n\}$, ``fills in'' a set $E \subset \mathbb{R}^d$ in an appropriate sense and investigate the degree to which the discrete analog to the Riesz energy of these sets can be used to bound the Hausdorff dimension of $E$. We also discuss applications to data science and Erdős/Falconer type problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limits of Discrete Energy of Families of Increasing Sets Nathan, Hari Sarang Classical Analysis and ODEs Machine Learning Metric Geometry The Hausdorff dimension of a set can be detected using the Riesz energy. Here, we consider situations where a sequence of points, $\{x_n\}$, ``fills in'' a set $E \subset \mathbb{R}^d$ in an appropriate sense and investigate the degree to which the discrete analog to the Riesz energy of these sets can be used to bound the Hausdorff dimension of $E$. We also discuss applications to data science and Erdős/Falconer type problems. |
| title | Limits of Discrete Energy of Families of Increasing Sets |
| topic | Classical Analysis and ODEs Machine Learning Metric Geometry |
| url | https://arxiv.org/abs/2504.11302 |