Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes...

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k into k nodes of degree 1. Four networks are considered, each evolves at each time step by either preferential attachment,...

The world-wide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scale-free characteristics. We introduce a...

In a discrete disordered system one is interested in computing the averaged Green's function 〈Gij〉. Using the supersymmetry formulation as a starting point, we derive a renormalization group flow equation for the effective probability distribution of a subsystem of fixed size, which...

We study chaotic functions that are exact solutions to nonlinear maps. A generalization of these functions (which cannot be expressed as a recursive procedure anymore) can produce truly random sequences. Even if the initial conditions are known exactly, the next values are in principle...

We analyse the influence of diagonal disorder (random site energy) on charge density wave (CDW) and superconductivity (SS) in local pair systems which are described by the model of hard core charged bosons on a lattice. This problem was previously studied within the mean field approximation for...

We investigate the critical behavior of a three-dimensional short-range spin-glass model in the presence of an external field ε conjugated to the Edwards–Anderson order parameter. In the mean-field approximation this model is described by the Adam–Gibbs–DiMarzio approach for the glass...

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study...

We determine the geometrical properties of the most probable paths at finite temperatures T, between two points separated by a distance r, in one-dimensional lattices with positive energies of interaction εi associated with bond i. The most probable path-length tmp in a homogeneous medium...

The motion of a particle confined within a strip (“flat pipe”) with diffusely-reflecting walls is analyzed in detail and provides a simple example of the interplay between randomness and geometrical constraint. The mean square dispersion Δx2 of the position is exactly found in various...