2020/10/22 by Douglas Hardin, Douglas P. Hardin, Hardin, Douglas +4
Decision Sciences · Mathematics · Physics and Astronomy · #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 #math-ph #math.CA #math.MG #math.MP #msc:28A78 #msc:31C20 #msc:52A40 #secondary
paper · pdf · doi:10.48550/arxiv.2010.11937
63 pages, 4 figures; corrected typos and clarified definition of the meshing algorithm
openalex publication_date 2020/10/22 · arxiv created 2021/03/25 · arxiv updated 2021/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a framework for extending the asymptotic behavior of a short-range interaction from the unit cube to general compact subsets of \mathbb Rd . 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.