Related papers: Spacing ratio characterization of the spectra of d…
Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length of the adjacency matrices of Erd\H{o}s-R\'enyi (ER) {\it fully}…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
Several spectral fluctuation measures of random matrix theory (RMT) have been applied in the study of spectral properties of networks. However, the calculation of those statistics requires performing an unfolding procedure, which may not be…
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…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erd\H{o}s-R\'enyi graphs. Our error bounds are sharp for a large class of sparse random matrices.…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
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…
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
We consider the ensemble of adjacency matrices of Erd\H{o}s-R\'{e}nyi random graphs, that is, graphs on $N$ vertices where every edge is chosen independently and with probability $p\equiv p(N)$. We rescale the matrix so that its bulk…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum {\bf 4}, 040312 (2023)]. Here, we perform a numerical study of the…
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree <k>, and p(s) undergoes a…
Complex networks with directed, local interactions are ubiquitous in nature, and often occur with probabilistic connections due to both intrinsic stochasticity and disordered environments. Sparse non-Hermitian random matrices arise…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…