Zipf's law from a Fisher variational-principle

Abstract

Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example we show that the number of citations found in the most referenced physics journals follows this law.

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• Space-time correlations in urban sprawl
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• The thermodynamics of urban population flows
• Variational Principle underlying Scale Invariant Social Systems
• Memory endowed US cities and their demographic interactions
• Inferring an optimal Fisher measure
• A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014
• Information and complexity measures in the interface of a metal and a superconductor
• Unravelling the size distribution of social groups with information theory on complex networks