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Power law distribution is common in real-world networks including online social networks. Many studies on complex networks focus on the characteristics of vertices, which are always proved to follow the power law. However, few researches…
The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidrv; the limiting rescaled spectral measure (LRSM)…
The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi-Hubbard model with dimerized hopping amplitude and find…
We compute the limiting eigenvalue statistics at the edge of the spectrum of large Hermitian random matrices perturbed by the addition of small rank deterministic matrices. To be more precise, we consider random Hermitian matrices with…
Network reconstruction is fundamental to understanding the dynamical behaviors of the networked systems. Many systems, modeled by multiplex networks with various types of interactions, display an entirely different dynamical behavior…
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…
Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex…
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 study the transition between layer-localized and delocalized regimes in a general contact-based contagion model on multiplex networks. Using the inverse participation ratio, we characterize how activity shifts from being confined to a…
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…
In this paper we demonstrate numerically that random networks whose adjacency matrices ${\bf A}$ are represented by a diluted version of the Power--Law Banded Random Matrix (PBRM) model have multifractal eigenfunctions. The PBRM model…
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…
We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation in random media.
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
We investigate MIMO eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly-correlated MIMO channel model, which does not require separable spatial correlations at the transmitter…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…
The eigenvalue distribution of the Hessian matrix plays a crucial role in understanding the optimization landscape of deep neural networks. Prior work has attributed the well-documented ``bulk-and-spike'' spectral structure, where a few…
In order to comprehend and enhance models that describes various brain regions is important to study the dynamics of trained recurrent neural networks. Including Dales law in such models usually presents several challenges. However, this is…