In the last twenty years, physicists and mathematicians developed and studied models for the wealth distribution using the classical tools of statistical physics: discrete and continuous stochastic processes (in particular, random exchange models) as well as related Boltzmann-type kinetic equations. In these works, the usual concept of equilibrium in Economics is either complemented or fully replaced by statistical equilibrium.
Here, I present a general framework to deal with distributional problems in Economics using random exchange models and a series of models based on this general framework. The framework makes use of random partitions of stocks and fragmentation-coagulation processes acting on these partitions. I start from finitary versions of these models and show how they naturally lead to continuous versions.
Bertram Düring, Nicos Georgiou, Enrico Scalas
A stylized model for wealth distribution
U. Garibaldi, E. Scalas
Finitary probabilistic models in Econophysics
Cambridge University Press, 2010.