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Abstract
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 language | English |
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Article number | 032408 |
Number of pages | 5 |
Journal | Physical Review E |
Volume | 98 |
Issue number | 3 |
Early online date | 12 Sept 2018 |
DOIs | |
Publication status | Published - 12 Sept 2018 |
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Dive into the research topics of 'Zipf's and Taylor's laws'. Together they form a unique fingerprint.Projects
- 1 Finished
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Dynamic equation approach to forecast long-range demographic scenarios
Simini, F. (Principal Investigator)
14/02/17 → 13/06/19
Project: Research