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© 2010

Theory of Zipf's Law and Beyond

Book

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 632)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 1-7
  3. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 9-18
  4. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 19-40
  5. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 41-57
  6. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 59-72
  7. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 73-95
  8. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 97-122
  9. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 123-145
  10. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 147-157
  11. Alexander Saichev, Yannick Malevergne, Didier Sornette
    Pages 159-166
  12. Back Matter
    Pages 1-5

About this book

Introduction

Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) time-varying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered.

Keywords

Birth and death processes Brownian motion Gibrat law Proportional growth Zipf's law geometric Brownian motion preferential attachment

Authors and affiliations

  1. 1.Mathematical Dept.State University of Nizhni NovgorodNizhny NovgorodRussian Federation
  2. 2.Inst. Supérieur d'Economie de, Administration et de Gestion (ISEAG)Université St.-EtienneSt.-Etienne CX 2France
  3. 3.Dept. Management,, Technologie und ÖkonomieETH ZürichZürichSwitzerland

Bibliographic information

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