Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets

TL;DR

This paper introduces a theory where extreme outliers, called dragon-kings, are modeled as Bose-Einstein condensates, explaining their occurrence alongside power-law distributions in various systems.

Contribution

It presents a novel theoretical framework linking outliers to Bose-Einstein condensation, unifying the understanding of power laws and exceptional events.

Findings

Dragon-kings are interpreted as Bose-Einstein condensates.

The theory explains coexistence of Zipf's law and outliers.

Large populations exhibit power-law distributions with outliers.

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.