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This book describes all aspects of quantitative approaches to urban population growth, ranging from measures and empirical results such as the famous Zipf law, to the mathematical description of their evolution.
List of contents
- PART I COUNTING PEOPLE
- 1: Urban population
- 1.1 Defining the city
- 1.2 An historical example: Paris
- 1.3 Functional and morphological denitions
- 1.4 Gridded population of the world
- 2: Why does population matter?
- 2.1 Population is a good start
- 2.2 Scaling in cities
- PART II RANKING CITIES
- 3: The distribution of urban populations
- 3.1 Power-laws
- 3.2 Zipf's law for cities
- 3.3 How to t a power-law?
- 3.4 Revisiting Zipf's law for cities
- 4: Dynamics of ranking
- 4.1 Stable versus unstable ranking
- 4.2 Modelling the ranking dynamics
- 4.3: Rank variations of cities
- PART III MODELS OF URBAN GROWTH
- 5: Stochastic calculus
- 5.1 Brownian motion
- 5.2 Itô and Stratonovich prescriptions
- 5.3 Fokker-Planck equation
- 6: Stochastic models of growth
- 6.1 Yule-Simon's model of growth
- 6.2 Gibrat's law for cities
- 6.3 Gabaix's mode
- 7: Models with migration
- 7.1 A modied Yule-Simon model
- 7.2 A master equation approach
- 7.3 Diusion with noise: the Bouchaud-Mezard model
- PART IV HOW CITIES TRULY GROW
- 8: The generalized central limit theorem and Levy stable laws
- 8.1 The central limit theorem and its generalization
- 8.2 Levy stable laws
- 8.3 The generalized central limit theorem
- 9: From First principles to the growth equation
- 9.1 Building a bottom-up equation
- 9.2 Gravitational model
- 9.3 Minimal model for the inter-urban migration flows
- 10: About city dynamics
- 10.1 Solving a new kind of equation
- 10.2 Analysis and scaling of the solution
- 10.3 Rank dynamics
- 11: Outlook: Beyond Zipf's law
- 11.1 Zipf's law: the end?
- 11.2 And space?
- References
- Index
About the author
Dr Marc Barthelemy is a former student of the École Normale Superieure of Paris and graduated at the University of Paris with a thesis in theoretical physics. His research focuses on complex systems with an emphasis on cities and networks. MB is research director at the Institute of Theoretical Physics (CEA) in Saclay and a member of the Center of Social Analysis and Mathematics (CAMS) at the Ecole des Hautes Etudes en Sciences Sociales (EHESS).
Dr Vincent Verbavatz is a former student of the École polytechnique and graduated at the University of Paris-Saclay with a thesis in statistical physics. His research focuses the modelling of cities, notably of the modelling of urban growth. VV is an associate researcher at Institut des systèmes complexes de Paris Île-de-France.
Summary
This book describes all aspects of quantitative approaches to urban population growth, ranging from measures and empirical results such as the famous Zipf law, to the mathematical description of their evolution.
