English
Related papers

Related papers: Spectra of large block matrices

200 papers

This paper introduces the concept of autonomous microring arbitration, or wavelength arbitration, to address the challenge of multi-microring initialization in microring-based Dense-Wavelength-Division-Multiplexed (DWDM) transceivers. This…

Hardware Architecture · Computer Science 2025-03-27 Sunjin Choi , Vladimir Stojanović

Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…

Probability · Mathematics 2010-11-16 Christopher Hammond , Steven J. Miller

In this paper, we study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint…

Probability · Mathematics 2018-09-17 Benoit Collins , Takahiro Hasebe , Noriyoshi Sakuma

We study the limiting spectral distribution of quantum channels whose Kraus operators are sampled as $n\times n$ random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with n, the…

Quantum Physics · Physics 2023-11-22 Cécilia Lancien , Patrick Oliveira Santos , Pierre Youssef

The density of complex eigenvalues of random asymmetric $N\times N$ matrices is found in the large-$N$ limit. The matrices are of the form $H_0+A$ where $A$ is a matrix of $N^2$ independent, identically distributed random variables with…

Condensed Matter · Physics 2009-10-28 Boris A Khoruzhenko

When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit…

Information Theory · Computer Science 2021-04-21 Fan Zhang , Khac-Hoang Ngo , Sheng Yang , Aria Nosratinia

In this paper, we discuss the computation of weighted max-min rate allocation using joint TDM/FDM strategies under a PSD mask constraint. We show that the weighted max-min solution allocates the rates according to a predetermined rate ratio…

Networking and Internet Architecture · Computer Science 2010-08-10 Ephi Zehavi , Amir Leshem , Ronny Levanda , Zhu Han

We study the distribution of complex eigenvalues $z_1,\ldots, z_N$ of random Hermitian $N\times N$ block band matrices with a complex deformation of a finite rank. Assuming that the width of the band $W$ grows faster than $\sqrt{N}$, we…

Mathematical Physics · Physics 2021-12-09 Mariya Shcherbina , Tatyana Shcherbina

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…

Random Schroedinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length n…

Mathematical Physics · Physics 2007-05-23 I. Ya. Goldsheid , B. A. Khoruzhenko

We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the…

Statistics Theory · Mathematics 2024-07-16 Emmanuel Chevallier

The empirical spectral distribution of Hermitian $K \times K$-block random matrices converges to a deterministic density on the real line with a potential atom at the origin as the dimension of the blocks tends to infinity. In this model…

Probability · Mathematics 2025-11-25 Markus Ebke , Torben Krüger

This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the…

Mathematical Physics · Physics 2013-07-04 Luca G Molinari

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

We derive new perturbation bounds for eigenvalues of Hermitian matrices with block structures. The structures we consider range from a standard 2-by-2 block form to block tridiagonal and tridigaonal forms. The main idea is the observation…

Numerical Analysis · Mathematics 2010-09-01 Yuji Nakatsukasa

We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…

Probability · Mathematics 2015-12-09 Matthias Löwe , Kristina Schubert

This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…

Information Theory · Computer Science 2019-05-07 Danilo Silva , Frank R. Kschischang , Ralf Kötter

In the present paper, we are concerned with the study of the spectral distribution of matrix-sequences showing a non-Hermitian block structure with Toeplitz blocks. We use the notion of geometric mean of matrices and the theory of…

Numerical Analysis · Mathematics 2026-04-07 Andrea Adriani , Giacomo Tento

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

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