Related papers: Localization, anomalous diffusion and slow relaxat…
We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…
We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…
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 study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint…
We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…
We give a method for taking microscopic limits of normal matrix ensembles. We apply this method to study the behaviour near certain types of singular points on the boundary of the droplet. Our investigation includes ensembles without…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special…
We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the…
The findings of X-ray and neutron scattering experiments on amorphous systems are interpreted within the framework of the theory of Euclidean random matrices. This allows to take into account the topological nature of the disorder, a key…
We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are…