当p/n→0时，大四元数样本协方差矩阵和相关矩阵的ESD具有强收敛性

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2020-04-01 DOI:10.1142/S2010326320500057

Xue Ding

{"title":"当p/n→0时，大四元数样本协方差矩阵和相关矩阵的ESD具有强收敛性","authors":"Xue Ding","doi":"10.1142/S2010326320500057","DOIUrl":null,"url":null,"abstract":"In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0\",\"authors\":\"Xue Ding\",\"doi\":\"10.1142/S2010326320500057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.\",\"PeriodicalId\":54329,\"journal\":{\"name\":\"Random Matrices-Theory and Applications\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Matrices-Theory and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S2010326320500057\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Matrices-Theory and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S2010326320500057","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

本文研究当总体维数[公式:见文]与样本量[公式:见文]之比趋于零时，大四元数样本协方差矩阵和相关矩阵的经验谱分布(ESD)的强收敛性。证明了重整四元数样本协方差矩阵的ESD几乎肯定地收敛于半圆律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0

In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.