The Statistics of -Statistics.

Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of -Statistics.

A generalization of the standard map and its statistical characterization.

From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. Several works on these maps, e.

An economically realistic asset exchange model.

Despite their highly idealized nature, certain agent-based models of asset exchange, proposed for the most part by physicists and mathematicians, have been shown to exhibit remarkable agreement with empirical wealth distribution data. While this agre- ement is comforting, there is widespread sentiment that further progress will require a detailed under- standing of the connection between these idealized models and the more realistic microeconomic models of exchange used by economists. In this paper, we examine that connection for a three-parameter asset exchange model, the Affine Wealth Model (AWM), that has demonstrated fraction-of-a-per cent agreement with empirical wealth data.

Simulation of a generalized asset exchange model with economic growth and wealth distribution.

The agent-based yard-sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a parameter λ. Our numerical results indicate that the model has a critical point at λ=1 between a phase for λ<1 with economic mobility and exponentially growing wealth of all agents and a nonstationary phase for λ≥1 with wealth condensation and no mobility.

The lattice Fokker-Planck equation for models of wealth distribution.

Recent work on agent-based models of wealth distribution has yielded nonlinear, non-local Fokker-Planck equations whose steady-state solutions describe empirical wealth distributions with remarkable accuracy using only a few free parameters. Because these equations are often used to solve the 'inverse problem' of determining the free parameters given empirical wealth data, there is much impetus to find fast and accurate methods of solving the 'forward problem' of finding the steady state corresponding to given parameters. In this work, we derive and calibrate a lattice Boltzmann equation for this purpose.