The universal macroscopic statistics and phase transitions of rank distributions |
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| Authors: | Iddo Eliazar Morrel H Cohen |
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| Institution: | 1. Department of Technology Management, 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;1. Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, B.C., V6T1Z1, Canada;2. Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland;1. Faculty of Science, Ningbo University of Technology, Ningbo, 315016, China;2. College of Information Technology, Ningbo Dahongying University, Ningbo, 315175, China;3. Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;4. Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;1. Department of Theoretical Physics and MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group, E?tv?s Loránd University, Budapest, Hungary;2. Wigner Research Centre for Physics, Budapest, Hungary |
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| 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. |
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