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

TL;DR

This paper explores the statistical behavior of identical interacting agents under a global constraint, deriving asymptotic distributions using geometrical methods and relating them to Gamma distributions in multi-agent systems.

Contribution

It introduces a geometrical approach to derive asymptotic distributions for agents in high-dimensional constrained systems, linking them to Gamma distributions and providing a volume formula for symmetrical bodies.

Findings

Derived asymptotic distribution using geometrical arguments.

Established connection between agent distributions and Gamma distributions.

Proposed a new formula for high-dimensional symmetrical body volume.

Abstract

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.