James, C, Azaele, S orcid.org/0000-0002-5153-4833, Maritan, A et al. (1 more author) (2018) Zipf's and Taylor's laws. Physical Review E, 98 (3). 032408. ISSN 2470-0045
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 American Physical Society. This is an author produced version of a paper published in Physical Review E. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Sep 2018 11:48 |
Last Modified: | 06 Oct 2018 02:53 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.98.032408 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135141 |