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We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio of the complex conductances of both phases. We propose an algorithm to determine the conductance of a finite network, in…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
Loewner matrix pencils play a central role in the system realization theory of Mayo and Antoulas, an important development in data-driven modeling. The eigenvalues of these pencils reveal system poles. How robust are the poles recovered via…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
We analyze when an arbitrary matrix pencil is equivalent to a dissipative Hamiltonian pencil and show that this heavily restricts the spectral properties. In order to relax the spectral properties, we introduce matrix pencils with…
We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…
We describe extensive computational experiments on spectral properties of random objects - random cubic graphs, random planar triangulations, and Voronoi and Delaunay diagrams of random (uniformly distributed) point sets on the sphere). We…
Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems…
We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
This paper focuses on large neural networks whose synaptic connectivity matrices are randomly chosen from certain random matrix ensembles. The dynamics of these networks can be characterized by the eigenvalue spectra of their connectivity…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
We study the spectral properties of matrices of long-range percolation model. These are N\times N random real symmetric matrices H=\{H(i,j)\}_{i,j} whose elements are independent random variables taking zero value with probability…
Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under…
We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure…
Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a…