Maximal Diversity and Zipf’s Law

Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increas...

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Bibliographic Details
Published in:Physical review letters 2021-09, Vol.127 (12), p.128301-128301, Article 128301
Main Authors: Mazzarisi, Onofrio, de Azevedo-Lopes, Amanda, Arenzon, Jeferson J., Corberi, Federico
Format: Article
Language:English
Subjects:
Empirical analysis
Linguistics
Size distribution
Statistical models
Zipf's Law
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Summary:Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps's law is discussed. As an example, we show that our analytical results compare very well with linguistics and population datasets.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.127.128301