Limits of Discrete Energy of Families of Increasing Sets

2025/04/15 by Hari Sarang Nathan, Nathan, Hari Sarang
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Mathematical Dynamics and Fractals #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2504.11302

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 ⊂ 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.

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