The oligarchic structure of Paretian Poisson processes

Abstract

Paretian Poisson processes are a mathematical model of random fractal populations governed by Paretian power law tail statistics, and connect together and underlie elemental issues in statistical physics. Considering Paretian Poisson processes to represent the wealth of individuals in human populations, we explore their oligarchic structure via the analysis of the following random ratios: the aggregate wealth of the oligarchs ranked from m+1 to n, measured relative to the wealth of the m-th oligarch (n> m). A mean analysis and a stochastic-limit analysis (as n→∞) of these ratios are conducted. We obtain closed-form results which turn out to be highly contingent on the fractal exponent of the Paretian Poisson process considered.