论文标题
短程相互作用功能的渐近特性
Asymptotic properties of short-range interaction functionals
论文作者
论文摘要
我们描述了一个框架，用于扩展从单位立方体到$ \ Mathbb r^d $的一般紧凑子集的短程相互作用的渐近行为。该框架使我们能够对高riesz能量和最佳量化器的渐近学进行统一的处理。我们进一步获得了有关比例不变最近的邻居相互作用的新结果，例如$ k $ - 最近的邻居截断了Riesz Energy。我们的广义方法应用于生成具有规定密度的分布的方法：强烈抑制的riesz能量，质心voronoi tessellations以及由于Persson和Strang引起的流行的Meshing算法。
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.
