Power-law connections: From Zipf to Heaps and beyond |
| |
Authors: | Iddo I Eliazar Morrel H Cohen |
| |
Institution: | 1. Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel;2. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019, USA;3. Department of Chemistry, Princeton University, Princeton, NJ 08544, USA |
| |
Abstract: | 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. |
| |
Keywords: | Rank distributions Pareto&rsquo s law Lorenz curves Innovation rates Phase transitions Self-organized criticality |
本文献已被 ScienceDirect 等数据库收录! |
|