Related papers: Eigenvalue ratio statistics of complex networks: D…
In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
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.
The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from…
The importance of the balance in inhibitory and excitatory couplings in the brain has increasingly been realized. Despite the key role played by inhibitory-excitatory couplings in the functioning of brain networks, the impact of a balanced…
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…
Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of random matrices (GOE), we investigate the interaction of the GOE with regular bound states. The eigenvalues of the latter may or may not be embedded in the GOE…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by…
We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of…
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…
We investigate the impact of degree-degree correlations on the spectra of networks. Even though density distributions exhibit drastic changes depending on the (dis)assortative mixing and the network architecture, the short range…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and…