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In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a…

Statistics Theory · Mathematics 2024-06-11 Patrice Abry , B. Cooper Boniece , Gustavo Didier , Herwig Wendt

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the…

Information Theory · Computer Science 2011-11-10 Reza Rashidi Far , Tamer Oraby , Wlodzimierz Bryc , Roland Speicher

This study derives a new property of the Wishart distribution when the degree-of-freedom and the size of the matrix parameter of the distribution grow simultaneoulsy. Particularly, the asymptotic normality of the product of four independent…

Statistics Theory · Mathematics 2022-03-29 Koji Tsukuda , Shun Matsuura

We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…

Classical Analysis and ODEs · Mathematics 2025-07-15 Luis Gomez , Jonathan Jaimangal , Azita Mayeli , Tasfia Proma

We studied universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues and the number of each of these eigenvalue goes to infinity in the asymptotic limit. In this case, the limiting eigenvalue distribution can be…

Probability · Mathematics 2008-12-16 M. Y. Mo

This paper centers on the limit eigenvalue distribution for random Vandermonde matrices with unit magnitude complex entries. The phases of the entries are chosen independently and identically distributed from the interval $[-\pi,\pi]$.…

Probability · Mathematics 2015-03-17 Gabriel H. Tucci , Philip A. Whiting

Diversity analysis of a number of Multiple-Input Multiple-Output (MIMO) applications requires the calculation of the expectation of a function whose variables are the ordered multiple eigenvalues of a Wishart matrix. In order to carry out…

Information Theory · Computer Science 2012-01-04 Hong Ju Park , Ender Ayanoglu

This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…

Methodology · Statistics 2023-08-15 Naoki Marumo , Takeru Matsuda , Yuto Miyatake

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…

Information Theory · Computer Science 2012-02-06 Lu Wei , Olav Tirkkonen , Prathapasinghe Dharmawansa , Matthew McKay

The purpose of this paper is to study the existence and uniqueness of solutions to a Stochastic Differential Equation (SDE) coming from the eigenvalues of Wishart processes. The coordinates are non-negative, evolve as Cox-Ingersoll-Ross…

Probability · Mathematics 2020-03-20 Benjamin Jourdain , Ezéchiel Kahn

We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…

Quantum Physics · Physics 2009-05-14 Ion Nechita

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic…

Probability · Mathematics 2013-03-14 Adrien Hardy , Arno B. J. Kuijlaars

A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits…

Statistics Theory · Mathematics 2019-12-09 Dandan Jiang , Jiang Hu , Zhiqiang Hou

For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…

Probability · Mathematics 2016-03-08 Costel Peligrad , Magda Peligrad

We define an indefinite Wishart matrix as a matrix of the form A=W^{T}W\Sigma, where \Sigma is an indefinite diagonal matrix and W is a matrix of independent standard normals. We focus on the case where W is L by 2 which has engineering…

Statistics Theory · Mathematics 2015-12-21 Ramis Movassagh , Alan Edelman

Let $X_N$ be a $N \times N$ real Wishart random matrix with aspect ratio $M/N$. The limit eigenvalue distribution of $X_N$ is the Marchenko-Pastur law with parameter $c = \lim_N M/N$. The limit moments $\{m_n\}_n$ are given by $m_n =…

Probability · Mathematics 2025-07-30 James A. Mingo , Josue Vazquez-Becerra

This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure…

Analysis of PDEs · Mathematics 2021-05-20 Charles Bertucci , Mérouane Debbah , Jean-Michel Lasry , Pierre-Louis Lions

It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical…

Mathematical Physics · Physics 2007-05-23 Craig A. Tracy , Harold Widom

A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density…

Statistics Theory · Mathematics 2016-09-08 Raimundas Vidunas , Akimichi Takemura

In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered…

Statistics Theory · Mathematics 2012-01-04 Emanuel Ben-David