On the Euclidean Distance between Two Gaussian Points and the Normal Covariogram of $$\boldsymbol{\mathbb{R}}^{\boldsymbol{d}}$$

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-04-09 DOI:10.3103/s1068362324010059

D. M. Martirosyan, V. K. Ohanyan

引用次数: 0

Abstract

The concept of covariogram is extended from bounded convex bodies in $\mathbb{R}^{d}$ to the entire space $\mathbb{R}^{d}$ by obtaining integral representations for the distribution and probability density functions of the Euclidean distance between two $d$-dimensional Gaussian points that have correlated coordinates governed by a covariance matrix. When $d=2$, a closed-form expression for the density function is obtained. Precise bounds for the moments of the considered distance are found in terms of the extreme eigenvalues of the covariance matrix.

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论两个高斯点与 $$\boldsymbol\{mathbb{R}}^{boldsymbol{d}}$ 的正态协方差图之间的欧氏距离

摘要协方差的概念从$\mathbb{R}^{d}$中的有界凸体扩展到了$\mathbb{R}^{d}$的整个空间，得到了两个$d$维高斯点之间欧氏距离的分布和概率密度函数的积分表示，这两个高斯点具有由协方差矩阵支配的相关坐标。当 $d=2$ 时，可以得到密度函数的闭式表达式。根据协方差矩阵的极值特征值，可以找到所考虑的距离矩的精确边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences MATHEMATICS-

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.