Theory and Applications of Random Matrix

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 30 November 2024 | Viewed by 836

Special Issue Editor


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Guest Editor
Department of Statistics, University of California, Davis, CA 95616, USA
Interests: high-dimensional statistics; random matrix theory; functional data analysis

Special Issue Information

Dear Colleagues,

I would like you to consider submitting a paper for publication in a Special Issue of Mathematics (published by MDPI) on the topic of Theory and Applications of Random Matrix. The purpose of this Special Issue is to publish high-quality papers within this broad theme within a fairly short period of time to ensure timeliness, a higher impact and a wider reach, beyond the traditional mathematics and statistics communities.

The submitted paper can fit into one of the following subtopics, although it need not be limited to these. 

  1. Application of random matrix theory in high-dimensional statistical inference.
  2. Random matrix models for dependent observations.
  3. High-dimensional principal components and canonical correlation analysis.
  4. Universality phenomena in random matrix theory.
  5. Application of free probability to the analysis of spectral behavior of large random matrices.

Prof. Dr. Debashis Paul
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • high-dimensional statistics
  • principal component analysis
  • canonical correlation analysis
  • limiting spectral distribution
  • linear spectral statistics
  • universality phenomena
  • free probability

 

Published Papers (1 paper)

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Review

11 pages, 340 KiB  
Review
Chi-Square Approximation for the Distribution of Individual Eigenvalues of a Singular Wishart Matrix
by Koki Shimizu and Hiroki Hashiguchi
Mathematics 2024, 12(6), 921; https://0-doi-org.brum.beds.ac.uk/10.3390/math12060921 - 20 Mar 2024
Viewed by 566
Abstract
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hypergeometric functions of matrix arguments. Furthermore, we show that the distribution of each eigenvalue can be approximated [...] Read more.
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hypergeometric functions of matrix arguments. Furthermore, we show that the distribution of each eigenvalue can be approximated by the chi-square distribution with varying degrees of freedom when the population eigenvalues are infinitely dispersed. The derived result is applied to testing the equality of eigenvalues in two populations. Full article
(This article belongs to the Special Issue Theory and Applications of Random Matrix)
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