Related papers: Statistical properties of mutualistic-competitive …
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…
The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…
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…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
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…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space.…
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 pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…