Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems

Ricardo López-Ruiz, Jaime Sañudo, Xavier Calbet
2009 Entropy  
A set of many identical interacting agents obeying a global additive constraint is considered. Under the hypothesis of equiprobability in the high-dimensional volume delimited in phase space by the constraint, the statistical behavior of a generic agent over the ensemble is worked out. The asymptotic distribution of that statistical behavior is derived from geometrical arguments. This distribution is related with the Gamma distributions found in several multi-agent economy models. The
more » ... dels. The parallelism with all these systems is established. Also, as a collateral result, a formula for the volume of high-dimensional symmetrical bodies is proposed.
doi:10.3390/e11040959 fatcat:eqefocmjafbevcbujcoghuf6ee