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Related papers: Spectra of large block matrices

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We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…

Mathematical Physics · Physics 2013-07-16 Motohisa Fukuda , Piotr Śniady

We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…

Operator Algebras · Mathematics 2014-07-25 Romuald Lenczewski

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 case, no closed-form expressions for…

Information Theory · Computer Science 2011-04-13 Florian Dupuy , Philippe Loubaton

Consider real symmetric, complex Hermitian Toeplitz and real symmetric Hankel band matrix models, where the bandwidth $b_{N}\ra \iy$ but $b_{N}/N \to b$, $b\in [0,1]$ as $N\to \infty$. We prove that the distributions of eigenvalues converge…

Probability · Mathematics 2009-11-02 Dang-Zheng Liu , Zheng-Dong Wang

The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the…

High Energy Physics - Theory · Physics 2015-05-28 Takao Suyama

The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…

Data Analysis, Statistics and Probability · Physics 2021-08-12 Udaysinh T. Bhosale , S. Harshini Tekur , M. S. Santhanam

This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…

Statistics Theory · Mathematics 2008-12-18 Alessandra Luati , Tommaso Proietti

In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…

Portfolio Management · Quantitative Finance 2016-05-24 Takashi Shinzato

We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are…

Condensed Matter · Physics 2009-10-28 E. Brézin , S. Hikami , A. Zee

In 2010, Silva, Kschischang and K\"otter studied certain classes of finite field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper we consider a generalisation of…

Information Theory · Computer Science 2018-02-01 Simon R. Blackburn , Jessica Claridge

We study the random matrices of type $\tilde{W}=(id\otimes\varphi)W$, where $W$ is a complex Wishart matrix of parameters $(dn,dm)$, and $\varphi:M_n(\mathbb C)\to M_n(\mathbb C)$ is a self-adjoint linear map. We prove that, under suitable…

Probability · Mathematics 2015-02-02 Teodor Banica , Ion Nechita

We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…

Information Theory · Computer Science 2008-06-24 Alessandro Nordio , Carla-Fabiana Chiasserini , Emanuele Viterbo

This paper studies the asymptotic behavior of eigenvalues of random abelian G-circulant matrices, that is, matrices whose structure is related to a finite abelian group G in a way that naturally generalizes the relationship between…

Probability · Mathematics 2012-08-17 Mark W. Meckes

We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input…

Disordered Systems and Neural Networks · Physics 2013-08-29 A. Goetschy , A. D. Stone

Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh…

Information Theory · Computer Science 2016-11-17 Giuseppe Durisi , Tobias Koch , Johan Östman , Yury Polyanskiy , Wei Yang

In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…

Statistics Theory · Mathematics 2021-04-27 Aya Shinozaki , Koki Shimizu , Hiroki Hashiguchi

We investigate the eigenstructure of matrix formulations used for modeling scattering processes within materials in transmission electron microscopy. Dynamical scattering is crucial for describing the interaction between an electron wave…

Materials Science · Physics 2025-12-12 Arya Bangun , Oleh Melnyk , Benjamin März

We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…

Mathematical Physics · Physics 2012-01-31 Dong Wang

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…

Disordered Systems and Neural Networks · Physics 2015-05-18 Ariel Amir , Yuval Oreg , Yoseph Imry

The performance analysis of random vector channels, particularly multiple-input-multiple-output (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of…

Information Theory · Computer Science 2015-01-05 Yuxin Chen , Andrea J. Goldsmith , Yonina C. Eldar