Maximal Diversity and Zipf's Law
Statistical Mechanics
2021-10-05 v2
Abstract
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' law is discussed. As an example, we show that our analytical results compare very well with linguistics datasets.
Keywords
Cite
@article{arxiv.2103.09143,
title = {Maximal Diversity and Zipf's Law},
author = {Onofrio Mazzarisi and Amanda de Azevedo-Lopes and Jeferson J. Arenzon and Federico Corberi},
journal= {arXiv preprint arXiv:2103.09143},
year = {2021}
}
Comments
5 pages, 3 figures