Related papers: Eigenvalue distribution analysis of multidimension…
The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to…
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…
The density of complex eigenvalues of random asymmetric $N\times N$ matrices is found in the large-$N$ limit. The matrices are of the form $H_0+A$ where $A$ is a matrix of $N^2$ independent, identically distributed random variables with…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, i.e. anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
Much effort has been spent on characterizing the spectrum of the non-backtracking matrix of certain classes of graphs, with special emphasis on the leading eigenvalue or the second eigenvector. Much less attention has been paid to the…
The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though…
In this paper we consider two-dimensional canonical systems with discrete spectrum and study their eigenvalue densities. We develop a formula that determines the Stieltjes transform of the eigenvalue counting function up to universal…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…
This paper is concerned with the asymptotic distribution of the largest eigenvalues for some nonlinear random matrix ensemble stemming from the study of neural networks. More precisely we consider $M= \frac{1}{m} YY^\top$ with $Y=f(WX)$…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…
We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the…
The propagation of waves through transmission eigenchannels in complex media is emerging as a new frontier of condensed matter and wave physics. A crucial step towards constructing a complete theory of eigenchannels is to demonstrate their…
This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common…
The study of correlated time-series is ubiquitous in statistical analysis, and the matrix decomposition of the cross-correlations between time series is a universal tool to extract the principal patterns of behavior in a wide range of…
Recently, an analytic method was developed to study in the large $N$ limit non-hermitean random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability distributions, thus extending the existing Gaussian…
We present efficient numerical techniques for calculation of eigenvalue distributions of random matrices in the beta-ensembles. We compute histograms using direct simulations on very large matrices, by using tridiagonal matrices with…