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Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street
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Stochastic equations and cities.

Marc Barthelemy1,2

  • 1Université Paris-Saclay, CEA, CNRS, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France.

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|July 5, 2023
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Summary
This summary is machine-generated.

Stochastic equations explain urban population dynamics, including deviations from Zipf's law and rank turbulence. Inter-urban migration shocks are crucial for understanding city population statistics and evolution.

Keywords:
citiescomplex systemsstochastic equations

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Area of Science:

  • Complex systems analysis
  • Urban dynamics modeling
  • Statistical physics applications

Background:

  • Stochastic equations are vital in science, particularly for complex systems like urban populations.
  • Zipf's law describes city populations, but recent data show deviations and turbulent rank dynamics.
  • Existing models like Gibrat and Gabaix offer partial explanations for urban population phenomena.

Purpose of the Study:

  • To review theoretical frameworks based on stochastic equations for urban population dynamics.
  • To explain deviations from Zipf's law and the turbulent evolution of city ranks.
  • To derive a first-principles stochastic equation for urban populations, emphasizing migration.

Main Methods:

  • Review of Gibrat and Gabaix models for urban population growth.
  • Analysis of phenomenological stochastic equations for rank dynamics and noise-induced transitions.
  • Derivation of a stochastic equation for city populations from first principles, incorporating migration.

Main Results:

  • Stochastic equations provide a unified framework for Zipf's law deviations and rank turbulence.
  • Phenomenological models capture rank variations and noise-induced transitions.
  • A derived stochastic equation highlights the critical role of inter-urban migration shocks.

Conclusions:

  • Stochastic equations are essential for understanding complex urban population dynamics.
  • Inter-urban migration is a key driver of city population statistics and evolution.
  • Further research can leverage these models for urban planning and policy.