English(EN) Limits of Discrete Energy of Families of Increasing Sets

新研究将 Riesz 能量与 Hausdorff 维度联系起来，用于数据科学应用

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-17 04:00

一篇新的研究论文探讨了集合的 Hausdorff 维度与 Riesz 能量离散模拟之间的关系。该研究已提交至 arXiv，研究了点集能量如何限制 Hausdorff 维度。文章还讨论了在数据科学和 Erdős/Falconer 类型问题中的潜在应用。 AI

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arXiv cs.LG TIER_1 English(EN) · Hari Sarang Nathan · 2026-07-17 04:00

递增集族离散能量的极限

arXiv:2504.11302v5 Announce Type: replace-cross 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 investiga…