Joint global fluctuations of complex Wigner and deterministic matrices

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2020-10-06 DOI:10.1142/S2010326322500150

C. Male, J. Mingo, S. P'ech'e, R. Speicher

引用次数: 7

Abstract

We characterize the limiting fluctuations of traces of several independent Wigner matrices and deterministic matrices under mild conditions. A CLT holds but in general the families are not asymptotically free of second-order and the limiting covariance depends the limiting [Formula: see text]-distribution of the deterministic matrices and their transposes and Hadamard products.

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复Wigner矩阵与确定性矩阵的联合全局波动

研究了几种独立Wigner矩阵和确定性矩阵在温和条件下的极限涨落。一个CLT成立，但一般来说，族不是渐近的二阶自由，极限协方差取决于确定性矩阵及其转置和Hadamard积的极限分布。

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

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.