Power laws are pervasive in economics and social sciences, particularly in the upper tails of distributions such as wealth, income, firm size, and city populations. Their scale-free property makes them a universal framework to understand phenomena spanning several orders of magnitude. This...

Power laws are pervasive in economics and social sciences, particularly in the upper tails of distributions such as wealth, income, firm size, and city populations. Their scale-free property makes them a universal framework to understand phenomena spanning several orders of magnitude. This...

We consider an evolving ensemble assembled from a set of n different elements via a stochastic growth process in which independent and identically distributed copies of the elements arrive randomly in time, and their statistics are governed by Zipf’s law. The associated “Heaps process” is...

In the literature, the deviations from standard behaviors of the solutions of the kinetic equation and the analogous diffusion equation are put forward by investigations which are carried out in the frame of fractional mathematics and nonextensive physics. On the other hand, the physical origins...

We simulate a model that captures all the features of the silver electrodeposition experiment in a rectangular cell. We study the bulk of the aggregates on the basis of a treeing process (M. Matsushita, P. Meakin, Cluster size distribution of self-affine fractals, Phys. Rev. A 37 (1988) 3645; F....

We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance r from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the mean, modulated by the local density ρ(r). The model is...