In the Cont–Bouchaud model [cond-mat/9712318] of stock markets, percolation clusters act as buying or selling investors and their statistics controls that of the price variations. Rather than fixing the concentration controlling each cluster connectivity artificially at or close to the...

We investigate the nonextensive q-distribution function for a gas in the presence of an external field of force possessing a potential U(r). In the case of a dilute gas, we show that the power-law distribution including the potential energy factor term can rigorously be deduced based on kinetic...

The analytical and computational studies of various isolated classical Hamiltonian systems including long-range interactions suggest that the N→∞ and t→∞ limits do not commute for entire classes of initial conditions. This is, for instance, the case for inertial planar rotators whenever...

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...

We use the formalism of “maximum principle of Shannon's entropy” to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean “internal order” (Boltzmann entropy) of a complex, self-interacting,...

A Monte Carlo computer simulation model is presented to study the evolution of stock price and the distribution of price fluctuation. The resistance is described by an elastic energy Ee=e·x2 resulting from the price deviation x from an initial value and the momentum trading by the potential...

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r>rδ corresponds...</1,>

We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display...

We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e., the increase of the number of new elementary business units and their size growth. We find a power-law relationship...