Asymptotic properties of short-range interaction functionals

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.

arXiv comment63 pages, 4 figures; corrected typos and clarified definition of the meshing algorithm

References in corpus (6)

• The sphere packing problem in dimension 24
• Hard-sphere melting and crystallization with event-chain Monte Carlo
• Concentration for Coulomb gases and Coulomb transport inequalities
• On global minimizers of repulsive-attractive power-law interaction energies
• On the Support of Minimizers of Causal Variational Principles
• Fast high-dimensional node generation with variable density

Cited by in corpus (2)

• Sphere packing bounds via rescaling
• Polarization and covering on sets of low smoothness