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Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets

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  • V. I. Yukalov
  • D. Sornette

Abstract

A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material failure, epileptic seizure intensities, and other systems. Within our theory, the large outliers are interpreted as droplets of Bose-Einstein condensate: the appearance of outliers is a natural consequence of the occurrence of Bose-Einstein condensation controlled by the relative degree of attraction, or utility, of the largest entities. For large populations, Zipf's law is recovered (except for the dragon-king outliers). The theory thus provides a parsimonious description of the possible coexistence of a power law distribution of event sizes (Zipf's law) and dragon-king outliers.

Suggested Citation

  • V. I. Yukalov & D. Sornette, 2012. "Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets," Papers 1205.1364, arXiv.org.
    • Handle: RePEc:arx:papers:1205.1364
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    References listed on IDEAS

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    1. Alex Saichev & Yannick Malevergne & Didier Sornette, 2010. "Theory of Zipf's Law and Beyond," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02946-2, December.
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    Cited by:

    1. Glette-Iversen, Ingrid & Aven, Terje, 2021. "On the meaning of and relationship between dragon-kings, black swans and related concepts," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    2. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "Optimal threshold for Pareto tail modelling in the presence of outliers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 169-180.

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