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arXiv · 2504.11302

Limits of Discrete Energy of Families of Increasing Sets

Hari Sarang Nathan
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Abstract

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 Erd\H{o}s/Falconer type problems.

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Hari Sarang Nathan. 2025-04-15. Limits of Discrete Energy of Families of Increasing Sets. https://arxiv.org/abs/2504.11302

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