切比雪夫滤波器
数学
格子(音乐)
统计的
概率分布
统计物理学
数学分析
统计
物理
声学
作者
Alexander Lai De Oliveira,Benjamin J. Binder
出处
期刊:Physical review
日期:2020-07-13
卷期号:102 (1)
被引量:2
标识
DOI:10.1103/physreve.102.012130
摘要
Pair correlation functions provide a summary statistic which quantifies the amount of spatial correlation between objects in a spatial domain. While pair correlation functions are commonly used to quantify continuous-space point processes, the on-lattice discrete case is less studied. Recent work has brought attention to the discrete case, wherein on-lattice pair correlation functions are formed by normalizing empirical pair distances against the probability distribution of random pair distances in a lattice with Manhattan and Chebyshev metrics. These distance distributions are typically derived on an ad hoc basis as required for specific applications. Here we present a generalized approach to deriving the probability distributions of pair distances in a lattice with discrete Manhattan and Chebyshev metrics, extending the Manhattan and Chebyshev pair correlation functions to lattices in $k$ dimensions. We also quantify the variability of the Manhattan and Chebyshev pair correlation functions, which is important to understanding the reliability and confidence of the statistic.
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