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Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two…
We introduce a class of models containing robust and analytically demonstrable multifractality induced by disorder correlations. Specifically, we investigate the statistics of eigenstates of disordered tight-binding models on two classes of…
The persistent current for a one-dimensional ring with two tunnel barriers is considered in the limit of weakly interacting electrons. In addition to a small off-resonance current, there are two kinds of resonant behavior; (i) a current…
For real world systems, nonuniform medium is ubiquitous. Therefore, we investigate the diffusion-limited-aggregation process on a two dimensional directed small-world network instead of regular lattice. The network structure is established…
We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…
The influence of fractal clusters of a normal phase on the current-voltage characteristics of a percolation superconductor in the region of a resistive transition has been studied. The clusters represent the aggregates of columnar defects,…
We study the fractal properties of the stationary distrubtion {\pi} for a simple Markov process on R. We will give bounds for the Hausdorff dimension of {\pi}, and lower bounds for the multifractal spectrum of {\pi}. Additionally, we will…
Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from…
This is a survey paper about the fractal percolation process, also known as Mandelbrot percolation. It is intended to give a general breadth overview of more recent research in the topic, but also includes some of the more classical…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of disordered systems, notably from the…
The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the…
We numerically study one-parameter family of random single-cluster systems. A finite-concentration topological phase transition from the net-like to the tree-like phase (the latter is without a backbone) is present in all models of the…
We study the spectrum of adjacency matrices of random graphs. We develop two techniques to lower bound the mass of the continuous part of the spectral measure or the density of states. As an application, we prove that the spectral measure…
We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al. [Nature 439, 828 (2006)], we consider a percolation process in which…
Ad-hoc networks are often deployed in regions with complicated boundaries. We show that if the boundary is modeled as a fractal, a network requiring line of sight connections has the counterintuitive property that increasing the number of…