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Related papers: Spectra of large block matrices

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Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-11-24 Nazar Emirov , Cheng Cheng , Qiyu Sun , Zhihua Qu

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh cases, no closed-form expressions for…

Information Theory · Computer Science 2010-07-07 Florian Dupuy , Philippe Loubaton

We study the limiting eigenvalue distribution of $n\times n$ banded Toeplitz matrices as $n\to \infty$. From classical results of Schmidt-Spitzer and Hirschman it is known that the eigenvalues accumulate on a special curve in the complex…

Complex Variables · Mathematics 2007-10-10 Maurice Duits , Arno B. J. Kuijlaars

In \cite{Diaz} beta type I and II doubly singular distributions were introduced and their densities and the joint densities of nonzero eigenvalues were derived. In such matrix variate distributions $p$, the dimension of two singular Wishart…

Statistics Theory · Mathematics 2020-01-07 Stepan Grinek

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

Disordered Systems and Neural Networks · Physics 2016-12-21 Alexander Kuczala , Tatyana O. Sharpee

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute…

Probability · Mathematics 2016-01-26 Octavio Arizmendi , Ion Nechita , Carlos Vargas

In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…

Information Theory · Computer Science 2015-07-29 Oliver James , Heung-No Lee

The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been…

Statistics Theory · Mathematics 2012-03-16 L. R. Haff , P. T. Kim , J. -Y. Koo , D. St. P. Richards

This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…

Statistics Theory · Mathematics 2021-01-25 Weiming Li , Qinwen Wang , Jianfeng Yao , Wang Zhou

A method for channel estimation in wideband massive Multiple-Input Multiple-Output (MIMO) systems using covariance identification is developed. The method is useful for Frequency-Division Duplex (FDD) at either sub-6GHz or millimeter wave…

Signal Processing · Electrical Eng. & Systems 2024-10-30 José González-Coma , Pedro Suárez-Casal , Paula M. Castro , Luis Castedo , Michael Joham

We investigate the maximal achievable rate for a given blocklength and error probability over quasi-static single-input multiple-output (SIMO) fading channels. Under mild conditions on the channel gains, it is shown that the channel…

Information Theory · Computer Science 2013-05-17 Wei Yang , Giuseppe Durisi , Tobias Koch , Yury Polyanskiy

We introduce two families of random tridiagonal block matrices for which the joint eigenvalue distributions can be computed explicitly. These distributions are novel within random matrix theory, and exhibit interactions among eigenvalue…

Probability · Mathematics 2026-05-18 Brian Rider , Benedek Valkó

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

In this paper, the multiple-input multiple-output (MIMO) transmit beampattern matching problem is considered. The problem is formulated to approximate a desired transmit beampattern (i.e., an energy distribution in space and frequency) and…

Optimization and Control · Mathematics 2018-02-21 Ziping Zhao , Daniel P. Palomar

We explore the limiting empirical eigenvalue distributions arising from matrices of the form \[A_{n+1} = \begin{bmatrix} A_n & I\\ I & A_n \end{bmatrix} , \]where $A_0$ is the adjacency matrix of a $k$-regular graph. We find that for…

Discrete Mathematics · Computer Science 2018-07-23 Clark Alexander , Tara Nenninger , Danielle Tucker

The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying…

Statistics Theory · Mathematics 2016-09-19 Axel Bücher , Johan Segers

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…

Computational Physics · Physics 2009-11-06 Anthony Hams , Hans De Raedt

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

Signal Processing · Electrical Eng. & Systems 2025-05-13 Augusto Aubry , Prabhu Babu , Antonio De Maio , Massimo Rosamilia

This paper investigates the performance of wireless systems that employ finite-blocklength channel codes for transmission and operate under queueing constraints in the form of limitations on buffer overflow probabilities. A block fading…

Information Theory · Computer Science 2010-10-01 Deli Qiao , Mustafa Cenk Gursoy , Senem Velipasalar

Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…

Statistics Theory · Mathematics 2025-07-08 Zeyan Zhuang , Xin Zhang , Dongfang Xu , Shenghui Song