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Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…

Mathematical Physics · Physics 2025-11-27 Gernot Akemann , Yan V. Fyodorov , Dmitry V. Savin

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…

Statistical Mechanics · Physics 2009-11-11 David S. Dean , Satya N. Majumdar

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a…

Mathematical Physics · Physics 2009-11-10 Romuald A. Janik , Waldemar Wieczorek

This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…

Statistics Theory · Mathematics 2021-01-25 Ziyang Lyu , A. H. Welsh

In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes.…

Statistics Theory · Mathematics 2012-11-08 Dietmar Bauer

In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all…

Mathematical Physics · Physics 2021-09-01 Yacin Ameur , Nam-Gyu Kang , Seong-Mi Seo

The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…

Probability · Mathematics 2017-02-23 Cagri Sert

We consider an ensemble of large non-Hermitian random matrices of the form $\hat{H}+i\hat{A}_s$, where $\hat{H}$ and $\hat{A}_s$ are Hermitian statistically independent random $N\times N$ matrices. We demonstrate the existence of a new…

Condensed Matter · Physics 2016-08-31 Yan V. Fyodorov , Boris A. Khoruzhenko , Hans-Juergen Sommers

The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges…

Probability · Mathematics 2016-03-09 Walid Hachem , Adrien Hardy , Jamal Najim

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

The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…

Statistics Theory · Mathematics 2012-04-16 Angelika Franke , Gerhard Osius

We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we…

Mathematical Physics · Physics 2015-07-16 Wojciech Mlotkowski , Maciej A. Nowak , Karol A. Penson , Karol Zyczkowski

We study the $k$-largest eigenvalues of heavy-tailed sample covariance matrices of the form $\bX\bX^\T$ in an asymptotic framework, where the dimension of the data and the sample size tend to infinity. To this end, we assume that the rows…

Probability · Mathematics 2013-09-13 Richard A. Davis , Oliver Pfaffel

We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…

Mathematical Physics · Physics 2018-08-20 Kevin Truong , Alexander Ossipov

For a broad class of unitary ensembles of random matrices we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting…

Probability · Mathematics 2008-04-08 Brian Rider , Xin Zhou

We consider linear spectral statistics built from the block-normalized correlation matrix of a set of $M$ mutually independent scalar time series. This matrix is composed of $M \times M$ blocks that contain the sample cross correlation…

Probability · Mathematics 2021-01-15 Philippe Loubaton , Xavier Mestre

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…

Probability · Mathematics 2007-05-23 Anatolii A. Puhalskii

The sum of Wishart matrices has an important role in multiuser communication employing multiantenna elements, such as multiple-input multiple-output (MIMO) multiple access channel (MAC), MIMO Relay channel, and other multiuser channels…

Information Theory · Computer Science 2018-03-13 S. Kumar , G. F. Pivaro , G. Fraidenraich , C. F. Dias

Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $\beta$-model to weighted graphs. Similar to the $\beta$-model, each vertex in maximum entropy models is assigned a potential parameter,…

Statistics Theory · Mathematics 2014-10-28 Ting Yan , Yunpeng Zhao , Hong Qin

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh