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We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…

Probability · Mathematics 2012-03-19 Olga Friesen , Matthias Löwe

We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…

Statistics Theory · Mathematics 2021-05-18 Weiming Li , Qinwen Wang , Jianfeng Yao

Stacked lensing is a powerful means of measuring the average mass distribution around large-scale structure tracers. There are two stacked lensing estimators used in the literature, denoted as $\Delta\Sigma$ and $\gamma_+$, which are…

Cosmology and Nongalactic Astrophysics · Physics 2018-06-06 Masato Shirasaki , Masahiro Takada

We establish a quantitative version of the Tracy--Widom law for the largest eigenvalue of high dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix…

Probability · Mathematics 2021-08-21 Kevin Schnelli , Yuanyuan Xu

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

We compare eigenvalue densities of Wigner random matrices whose elements are independent identically distributed (iid) random numbers with a Levy distribution and maximally random matrices with a rotationally invariant measure exhibiting a…

Statistical Mechanics · Physics 2013-05-29 Zdzislaw Burda , Jerzy Jurkiewicz , Maciej A. Nowak , Gabor Papp , Ismail Zahed

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…

Statistics Theory · Mathematics 2023-12-25 Qianqian Jiang , Jiaxin Qiu , Zeng Li

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

Disordered Systems and Neural Networks · Physics 2026-05-21 Yaprak Önder , Abbas Ali Saberi , Roderich Moessner

We study high-dimensional sample covariance matrices based on independent random vectors with missing coordinates. The presence of missing observations is common in modern applications such as climate studies or gene expression…

Probability · Mathematics 2016-03-01 Kamil Jurczak , Angelika Rohde

We consider sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2} X)^*$, where the sample $X$ is an $M\times N$ random matrix whose entries are real independent random variables with variance $1/N$ and where…

Probability · Mathematics 2015-06-10 Ji Oon Lee , Kevin Schnelli

Improving the efficiency of discrete time scale invariant (DSI) processes, we consider some flexible sampling of a continuous time DSI process ${X(t), t\in{R^+}}$ with scale $l>1$, which is in correspondence to some multi-dimensional…

Probability · Mathematics 2013-01-03 N . Modarresi , S . Rezakhah

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary…

Statistical Mechanics · Physics 2009-10-31 Gregory Brown , Per Arne Rikvold , Mark Sutton , Martin Grant

We consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity. More precisely, let $X$ be an…

Probability · Mathematics 2009-09-29 Noureddine El Karoui

We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn…

Statistical Mechanics · Physics 2026-03-05 Maximilien Bernard , Pierre Le Doussal , Alberto Rosso , Christophe Texier

Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…

Statistics Theory · Mathematics 2022-12-09 J. W. Silverstein , P. L. Combettes

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…

Condensed Matter · Physics 2009-10-28 Daniel A. Hamburger-Lidar

We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of…

Mathematical Physics · Physics 2015-05-13 Delphine Féral , Sandrine Péché

The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L}…

Statistical Mechanics · Physics 2009-11-07 Subhadip Raychaudhuri , Michael Cranston , Corry Pryzybla , Yonathan Shapir

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…

Statistics Theory · Mathematics 2018-03-22 Jiang Hu , Weiming Li , Zhi Liu , Wang Zhou

We find a simple, accurate model for the covariance matrix of the real-space cosmological matter power spectrum on slightly nonlinear scales (k~0.1-0.8 h/Mpc at z=0), where off-diagonal matrix elements become substantial. The model includes…

Cosmology and Nongalactic Astrophysics · Physics 2011-06-30 Mark C. Neyrinck