The universal macroscopic statistics and phase transitions of rank distributions

Iddo Eliazar and Morrel H. Cohen

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 23, 4293-4303

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.

Keywords: Rank distributions; Lorenz curves; Regular variation; Lorenzian Limit Law (LLL); Central Limit Theorem (CLT); Universality; Power-laws; Pareto’s law; Zipf’s law; Network topologies; Socioeconomic states; Phase transitions; Self-organized criticality (SOC) (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:23:p:4293-4303

DOI: 10.1016/j.physa.2011.06.049

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