Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Theory and Applications of Random Matrix
share announcement

Theory and Applications of Random Matrix

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 6983

Special Issue Editor

Prof. Dr. Debashis Paul

E-Mail Website
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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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

 

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

24 pages, 366 KiB  
Article
The Exact Density of the Eigenvalues of the Wishart and Matrix-Variate Gamma and Beta Random Variables
by A. M. Mathai and Serge B. Provost
Mathematics 2024, 12(15), 2427; https://doi.org/10.3390/math12152427 - 5 Aug 2024
Viewed by 817
Abstract
The determination of the distributions of the eigenvalues associated with matrix-variate gamma and beta random variables of either type proves to be a challenging problem. Several of the approaches utilized so far yield unwieldy representations that, for instance, are expressed in terms of [...] Read more.
The determination of the distributions of the eigenvalues associated with matrix-variate gamma and beta random variables of either type proves to be a challenging problem. Several of the approaches utilized so far yield unwieldy representations that, for instance, are expressed in terms of multiple integrals, functions of skew symmetric matrices, ratios of determinants, solutions of differential equations, zonal polynomials, and products of incomplete gamma or beta functions. In the present paper, representations of the density functions of the smallest, largest and jth largest eigenvalues of matrix-variate gamma and each type of beta random variables are explicitly provided as finite sums when certain parameters are integers and, as explicit series, in the general situations. In each instance, both the real and complex cases are considered. The derivations initially involve an orthonormal or unitary transformation whereby the wedge products of the differential elements of the eigenvalues can be worked out from those of the original matrix-variate random variables. Some of these results also address the distribution of the eigenvalues of a central Wishart matrix as well as eigenvalue problems arising in connection with the analysis of variance procedure and certain tests of hypotheses in multivariate analysis. Additionally, three numerical examples are provided for illustration purposes. Full article
(This article belongs to the Special Issue Theory and Applications of Random Matrix)
►▼ Show Figures

Figure 1

41 pages, 1269 KiB  
Article
Entry-Wise Eigenvector Analysis and Improved Rates for Topic Modeling on Short Documents
by Zheng Tracy Ke and Jingming Wang
Mathematics 2024, 12(11), 1682; https://doi.org/10.3390/math12111682 - 28 May 2024
Viewed by 4220
Abstract
Topic modeling is a widely utilized tool in text analysis. We investigate the optimal rate for estimating a topic model. Specifically, we consider a scenario with n documents, a vocabulary of size p, and document lengths at the order N. When [...] Read more.
Topic modeling is a widely utilized tool in text analysis. We investigate the optimal rate for estimating a topic model. Specifically, we consider a scenario with n documents, a vocabulary of size p, and document lengths at the order N. When N≥c·p, referred to as the long-document case, the optimal rate is established in the literature at p/(Nn). However, when N=o(p), referred to as the short-document case, the optimal rate remains unknown. In this paper, we first provide new entry-wise large-deviation bounds for the empirical singular vectors of a topic model. We then apply these bounds to improve the error rate of a spectral algorithm, Topic-SCORE. Finally, by comparing the improved error rate with the minimax lower bound, we conclude that the optimal rate is still p/(Nn) in the short-document case. Full article
(This article belongs to the Special Issue Theory and Applications of Random Matrix)
►▼ Show Figures

Figure 1

11 pages, 341 KiB  
Article
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://doi.org/10.3390/math12060921 - 20 Mar 2024
Viewed by 1277
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)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop