Asymptotic properties of short-range interaction functionals

2020/10/22 by Douglas P. Hardin, Edward B. Saff, Hardin, Douglas +3
Decision Sciences · Mathematics · #28A78 #31C20 #52A40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Primary #Probabilistic and Robust Engineering Design #secondary

paper · pdf · doi:10.48550/arxiv.2010.11937

openalex publication_date 2020/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a framework for extending the asymptotic behavior of a short-range interaction from the unit cube to general compact subsets of \mathbb R^d . This framework allows us to give a unified treatment of asymptotics of hypersingular Riesz energies and optimal quantizers. We further obtain new results about the scale-invariant nearest neighbor interactions, such as the k -nearest neighbor truncated Riesz energy. Our generalized approach has applications to methods for generating distributions with prescribed density: strongly-repulsive Riesz energies, centroidal Voronoi tessellations, and a popular meshing algorithm due to Persson and Strang.

Citations

• Centroidal Voronoi Tessellations: Applications and Algorithms
• Minimal Riesz energy point configurations for rectifiable d -dimensional manifolds

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