Statistics and Dynamics of Urban Populations
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Statistics and Dynamics of Urban Populations
Empirical Results and Theoretical Approaches
Verbavatz, Vincent; Barthelemy, Marc
Oxford University Press
12/2023
176
Dura
Inglês
9780192867544
15 a 20 dias
Descrição não disponível.
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 Ito 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
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 Ito 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
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
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 Ito 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
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 Ito 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
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