相关论文: Spectral analysis of large dimensional Chatterjee'…

We study the eigenvalue of the Wigner random matrix, which is created from a time series with temporal correlation. We observe the deformation of the semi-circle law which is similar to the eigenvalue distribution of the Wigner-L\`{e}vy…

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…

We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…

We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be…

For two lacunary sequences $(M_{n,1})_{n\geq 2},(M_{n,2})_{n\geq 0}$ and suitable functions $f$ we introduce random matrix ensembles with \begin{equation*} X_{n,n'}=f(M_{n+n',1}x_1,M_{|n-n'|,2}x_2). \end{equation*} We prove weak convergence…

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…

It has been shown that, if a model displays long-range (power-law) spatial correlations, its equal-time correlation matrix of this model will also have a power law tail in the distribution of its high-lying eigenvalues. The purpose of this…

We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in its ciritical region. By studying the spectral…

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic…

In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension of the Kendall rank correlation coefficient. We establish the…

The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…

Let $\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\le j\le k\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix…

Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…

This short paper reports some initial experimental demonstrations of the theoretical framework: the massive amount of data in the large-scale cognitive radio network can be naturally modeled as (large) random matrices. In particular, using…

Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…

We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…

We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

Let $\mathbf X=(X_{jk})$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\le j\le k$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\mathbf X$ to the…