Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible
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Physics Department, Sapienza University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy
2
Sony Computer Science Laboratories, 6, rue Amyot, 75005 Paris, France
3
Complexity Science Hub Vienna, Josefstädter Strasse 39, A-1080 Vienna, Austria
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(10), 752; https://doi.org/10.3390/e20100752
Received: 31 July 2018
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Revised: 17 September 2018
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Accepted: 25 September 2018
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Published: 30 September 2018
(This article belongs to the Special Issue Economic Fitness and Complexity)
Zipf’s, Heaps’ and Taylor’s laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that accounts for the emergence of those laws without deducing the emergence of one of the laws from the others or without ad hoc assumptions. This modeling framework is based on the concept of adjacent possible space and its key feature of being dynamically restructured while its boundaries get explored, i.e., conditional to the occurrence of novel events. Here, we illustrate this approach and show how this simple modeling framework, instantiated through a modified Pólya’s urn model, is able to reproduce Zipf’s, Heaps’ and Taylor’s laws within a unique self-consistent scheme. In addition, the same modeling scheme embraces other less common evolutionary laws (Hoppe’s model and Dirichlet processes) as particular cases.
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Keywords:
innovation dynamics; stylized facts; Zipf’s law; Heaps’ law, Taylor’s law; adjacent possible; Pólya’s Urns; Poisson-Dirichlet processes
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MDPI and ACS Style
Tria, F.; Loreto, V.; Servedio, V.D.P. Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible. Entropy 2018, 20, 752. https://doi.org/10.3390/e20100752
AMA Style
Tria F, Loreto V, Servedio VDP. Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible. Entropy. 2018; 20(10):752. https://doi.org/10.3390/e20100752
Chicago/Turabian StyleTria, Francesca, Vittorio Loreto, and Vito D. P. Servedio. 2018. "Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible" Entropy 20, no. 10: 752. https://doi.org/10.3390/e20100752
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