Statistics and Dynamics of Urban Populations

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