Zipf's and Taylor's laws

Charlotte R James, Sandro Azaele, Amos Maritan, Filippo Simini

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)
180 Downloads (Pure)


Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. Empirical evidence of the validity of these laws has been found in many and diverse domains. Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of individual dynamics without fine-tuning. Here we show that Zipf's law and Taylor's law can emerge from a general class of stochastic processes at the individual level, which incorporate one of two features: environmental variability, i.e., fluctuations of parameters, or correlations, i.e., dependence between individuals. Under these assumptions, we show numerically and with theoretical arguments that the conditional variance of the population increments scales as the square of the population, and that the corresponding stationary distribution of the processes follows Zipf's law.

Original languageEnglish
Article number032408
Number of pages5
JournalPhysical Review E
Issue number3
Early online date12 Sep 2018
Publication statusPublished - 12 Sep 2018

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