相关论文: Tails of Random Matrix Diagonal Elements: The Case…

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues…

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…

We compute analytically, for large $N$, the probability $\mathcal{P}(N_+,N)$ that a $N\times N$ Wishart random matrix has $N_+$ eigenvalues exceeding a threshold $N\zeta$, including its large deviation tails. This probability plays a…

We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $\beta$-ensembles in three cases : the case of Wigner matrices without Gaussian tails, that is Wigner…

We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…

In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…

This paper is concerned with the statistical properties of the Gram matrix $\mathbf{W}=\mathbf{H}\mathbf{H}^\dagger$, where $\mathbf{H}$ is a $2\times2$ complex central Gaussian matrix whose elements have arbitrary variances. With such…

We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…

This paper develops an efficient Monte Carlo method to estimate the tail probabilities of the ratio of the largest eigenvalue to the trace of the Wishart matrix, which plays an important role in multivariate data analysis. The estimator is…

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…

A Wishart matrix is said to be spiked when the underlying covariance matrix has a single eigenvalue $b$ different from unity. As $b$ increases through $b=2$, a gap forms from the largest eigenvalue to the rest of the spectrum, and with…

The paper "An efficient sampling scheme for the eigenvalues of dual Wishart matrices", by I.~Santamar\'ia and V.~Elvira, [\emph{IEEE Signal Processing Letters}, vol.~28, pp.~2177--2181, 2021] \cite{SE21}, poses the question of efficient…

We investigate whether the Wigner semi-circle and Marcenko-Pastur distributions, often used for deep neural network theoretical analysis, match empirically observed spectral densities. We find that even allowing for outliers, the observed…

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.

We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of $C$ are independent and…

Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices is formed by the adjacency matrix of an Erd\H{o}s-R\'{e}nyi graph $\mathcal{G}_{n,p}$ equipped with i.i.d.…

Consider a random symmetric matrix with i.i.d.~entries on and above its diagonal that are products of Bernoulli random variables and random variables with sub-Gaussian tails. Such a matrix will be called a sparse Wigner matrix and can be…

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…

The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…

The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of…