Issue
EPL
Volume 83, Number 4, August 2008
Article Number 40004
Number of page(s) 4
Section General
DOI http://dx.doi.org/10.1209/0295-5075/83/40004
Published online 06 August 2008
EPL, 83 (2008) 40004
DOI: 10.1209/0295-5075/83/40004

The oligarchic structure of Paretian Poisson processes

I. Eliazar1 and J. Klafter2

1  Department of Technology Management, Holon Institute of Technology - P.O. Box 305, Holon 58102, Israel
2  School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University - Tel Aviv 69978, Israel

eliazar@post.tau.ac.il
klafter@post.tau.ac.il

received 1 May 2008; accepted in final form 27 June 2008; published August 2008
published online 6 August 2008

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\rightarrow \infty $) 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.

PACS
02.50.-r - Probability theory, stochastic processes, and statistics.
05.45.Df - Fractals.
05.65.+b - Self-organized systems.

© EPLA 2008