Maximal Diversity and Zipf’s Law
Onofrio Mazzarisi, Amanda de Azevedo-Lopes, Jeferson J. Arenzon, Federico Corberi
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's law is discussed. As an example, we show that our analytical results compare very well with linguistics and population datasets.
Topics & Concepts
Zipf's lawDiversity (politics)MaximizationDimension (graph theory)Relation (database)Statistical physicsLawComponent (thermodynamics)MathematicsComputer scienceStatisticsPhysicsCombinatoricsPolitical scienceMathematical optimizationData miningQuantum mechanicsComplex Network Analysis TechniquesLanguage and cultural evolution