{"title":"Joint global fluctuations of complex Wigner and deterministic matrices","authors":"C. Male, J. Mingo, S. P'ech'e, R. Speicher","doi":"10.1142/S2010326322500150","DOIUrl":null,"url":null,"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.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":"57 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Matrices-Theory and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S2010326322500150","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: 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.
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.
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