The universal macroscopic statistics and phase transitions of rank distributions

Iddo Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We establish a "Central Limit Theorem" for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the "Lorenzian Limit Law" (LLL). Applications of the LLL further establish: (i) a statistical explanation for the universal emergence of Pareto's law in the context of rank distributions; (ii) a statistical classification of universal macroscopic network topologies; (iii) a statistical classification of universal macroscopic socioeconomic states; (iv) a statistical classification of Zipf's law, and a characterization of the "self-organized criticality" it manifests.

Original languageEnglish (US)
Pages (from-to)4293-4303
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
Volume390
Issue number23-24
DOIs
StatePublished - Nov 1 2011

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Keywords

  • Central Limit Theorem (CLT)
  • Lorenz curves
  • Lorenzian Limit Law (LLL)
  • Network topologies
  • Pareto's law
  • Phase transitions
  • Power-laws
  • Rank distributions
  • Regular variation
  • Self-organized criticality (SOC)
  • Socioeconomic states
  • Universality
  • Zipf's law

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