The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of...

Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation...

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian...

We show that within classical statistical mechanics, without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical distributions have to be separated from the total system energy,...

Some general features of statistical multi-agent economic models are reviewed, with particular attention to the dependence of the equilibrium wealth distribution on the agents’ saving propensities. It is shown that in a finite system of agents with a continuous saving propensity distribution a...

This work studies the Zipf law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in Brazilian cities does follow a power-law similar to the...

We present a study of three large object-oriented software systems—VisualWorks Smalltalk, Java JDK and Eclipse—searching for scaling laws in some of their properties. We study four system properties related to code production, namely the inheritance hierarchies, the naming of variables and...

Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously...

Motivated by the question “how equal is the distribution of wealth within a given human population?” economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the Lorenz curve and the following indices: Gini, Pietra, Hoover, Amato, Hirschman,...

From the Old Testament to the Communist Manifesto, and from the French Revolution to the Occupy Wall Street protests, social inequality has always been at the focal point of public debate, as well as a major driver of political change. Although being of prime interest since Biblical times, the...