Theory of Zipf's law and beyond

zbMath1189.91009MaRDI QIDQ1039386

Didier Sornette, Yannick Malevergne, Alexander I. Saichev

Publication date: 30 November 2009

Published in: Lecture Notes in Economics and Mathematical Systems (Search for Journal in Brave)

zbMATH Keywords

diffusion processrenewal processgeometric Brownian motionZipf's lawsteady-state densityproportional growthstochastically decaying processstochastically growing process

Mathematics Subject Classification ID

Applications of statistics to economics (62P20) Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance (91-02) Trade models (91B60) Diffusion processes (60J60) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20) Matching models (91B68)

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Kinetic and mean field description of Gibrat's law ⋮ Prediction and prevention of disproportionally dominant agents in complex networks ⋮ A scaling law beyond Zipf's law and its relation to Heaps' law ⋮ Majorization, ``useful Csiszár divergence and ``useful Zipf-Mandelbrot law ⋮ Zipf's law and maximum sustainable growth ⋮ Generalised central limit theorems for growth rate distribution of complex systems ⋮ Matrix Kesten recursion, inverse-Wishart ensemble and fermions in a Morse potential

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