IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i23p4293-4303.html
   My bibliography  Save this article

The universal macroscopic statistics and phase transitions of rank distributions

Author

Listed:
  • Eliazar, Iddo
  • Cohen, Morrel H.

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.

Suggested Citation

  • Eliazar, Iddo & Cohen, Morrel H., 2011. "The universal macroscopic statistics and phase transitions of rank distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4293-4303.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4293-4303
    DOI: 10.1016/j.physa.2011.06.049
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111004961
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2011.06.049?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bouchaud,Jean-Philippe & Potters,Marc, 2009. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521741866, October.
    2. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. G., Mauricio Contreras & Peña, Juan Pablo, 2019. "The quantum dark side of the optimal control theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 450-473.
    2. Eliazar, Iddo, 2014. "From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 479-492.
    3. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.
    4. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    5. Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    6. Lee, Jae Woo & Eun Lee, Kyoung & Arne Rikvold, Per, 2006. "Multifractal behavior of the Korean stock-market index KOSPI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 355-361.
    7. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    8. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    9. David Vidal-Tomás & Simone Alfarano, 2020. "An agent-based early warning indicator for financial market instability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 49-87, January.
    10. Demidov, Denis & Frahm, Klaus M. & Shepelyansky, Dima L., 2020. "What is the central bank of Wikipedia?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    11. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    12. Joachim Kaldasch, 2015. "Dynamic Model of the Price Dispersion of Homogeneous Goods," Papers 1509.01216, arXiv.org.
    13. Wang, Guochao & Zheng, Shenzhou & Wang, Jun, 2019. "Complex and composite entropy fluctuation behaviors of statistical physics interacting financial model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 97-113.
    14. Jung, Woo-Sung & Kwon, Okyu & Wang, Fengzhong & Kaizoji, Taisei & Moon, Hie-Tae & Stanley, H. Eugene, 2008. "Group dynamics of the Japanese market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 537-542.
    15. Arthur Matsuo Yamashita Rios de Sousa & Hideki Takayasu & Misako Takayasu, 2017. "Detection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-18, May.
    16. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    17. Pištěk, Miroslav & Slanina, František, 2011. "Diversity of scales makes an advantage: The case of the Minority Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2549-2561.
    18. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
    19. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 255-272, October.
    20. Gautier Marti & Frank Nielsen & Philippe Donnat & S'ebastien Andler, 2016. "On clustering financial time series: a need for distances between dependent random variables," Papers 1603.07822, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4293-4303. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.