Multi-agent systems, Equiprobability, Gamma distributions and other Geometrical questions

Details Multi-agent systems, Equiprobability, Gamma distributions and other Geometrical questions Multi-agent systems, Equiprobability, Gamma distributions and other Geometrical questions

2007-08-28

arxiv.org/abs/0708.3761v2

Nonlinear Sciences

Chaotic Dynamics

15 pages, 3 figures

Scientific paper

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 parallelism with all these systems is established. Also, as a collateral result, a formula for the volume of high-dimensional symmetrical bodies is proposed.

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