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New research links Riesz energy to Hausdorff dimension for data science applications

By PulseAugur Editorial · [1 sources] ·

A new research paper explores the relationship between the Hausdorff dimension of a set and the discrete analog of Riesz energy. The study, submitted to arXiv, investigates how the energy of increasing sets of points can bound the Hausdorff dimension. Potential applications in data science and Erdős/Falconer type problems are also discussed. AI

RANK_REASON The cluster contains a single arXiv research paper submission. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New research links Riesz energy to Hausdorff dimension for data science applications

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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Hari Sarang Nathan ·

    Limits of Discrete Energy of Families of Increasing Sets

    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…

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