Power-law connections: From Zipf to Heaps and beyond

Iddo I. Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf's law, Pareto's law, and Heaps' law-three elemental empirical power-laws that are ubiquitously observed in the sciences.

Original languageEnglish (US)
Pages (from-to)56-74
Number of pages19
JournalAnnals of Physics
StatePublished - May 2012

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Innovation rates
  • Lorenz curves
  • Pareto's law
  • Phase transitions
  • Rank distributions
  • Self-organized criticality


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