Related papers: How much random a random network is : a random mat…

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…

Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…

Network analysis provides powerful tools to learn about a variety of social systems. However, most analyses implicitly assume that the considered relational data is error-free, reliable and accurately reflects the system to be analysed.…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…

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…

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…

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…

Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…

The possibility to identify the nature (e.g. random or scale free) of complex networks while performing respective random walks is investigated with respect to autonomous agents based on Bayesian decision theory and humans navigating…

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter $\beta>1$, of the basic Toeplitz matrix-sequence…

Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for…

We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…

Time-fluctuating signals are ubiquitous and diverse in many physical, chemical, and biological systems, among which random telegraph signals (RTSs) refer to a series of instantaneous switching events between two discrete levels from…