Power-law connections: From Zipf to Heaps and beyond

被引：12

作者：

Eliazar, Iddo I. ^{[1
]}

Cohen, Morrel H. ^{[2
,3
]}

机构：

[1] Holon Inst Technol, IL-58102 Holon, Israel

[2] Rutgers State Univ, Dept Phys & Astron, Piscataway, NJ 08854 USA

[3] Princeton Univ, Dept Chem, Princeton, NJ 08544 USA

来源：

ANNALS OF PHYSICS | 2013年 / 332卷

关键词：

Rank distributions; Pareto's law; Lorenz curves; Innovation rates; Phase transitions; Self-organized criticality; ANOMALOUS DIFFUSION; DISTRIBUTIONS; EXPLANATION; STATISTICS; DYNAMICS; GROWTH; MODEL;

D O I：

10.1016/j.aop.2013.01.013

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 Zipfs law, Pareto's law, and Heaps' law three elemental empirical power-laws that are ubiquitously observed in the sciences. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：56 / 74

页数：19

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