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Related Experiment Videos

Some distributions associated with bose-einstein statistics.

Y Ijiri1, H A Simon

  • 1Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1975
PubMed
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This study introduces a stochastic process for Bose-Einstein statistics, linking Gibrat's Law to city growth phenomena. It derives geometric and Yule distributions, simplifying Pareto Law acquisition from Bose-Einstein statistics.

Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Urban Dynamics

Background:

  • Bose-Einstein statistics are fundamental in quantum mechanics and statistical physics.
  • Gibrat's Law describes proportional growth, often observed in economic and biological systems.
  • Understanding city size distributions is crucial for urban planning and socioeconomic analysis.

Purpose of the Study:

  • To develop a novel stochastic process model for Bose-Einstein statistics.
  • To investigate the relationship between Gibrat's Law and Bose-Einstein statistics.
  • To apply the derived distributions to model city size and growth patterns.

Main Methods:

  • Formulating a stochastic process based on Gibrat's Law.
  • Deriving steady-state conditions under different boundary conditions.

Related Experiment Videos

  • Analyzing the resulting geometric and Yule distributions.
  • Comparing the new Pareto Law derivation with existing methods.

    • Main Results:

    • The stochastic process yields the geometric distribution under specific boundary conditions.
    • The Yule distribution is derived under alternative boundary conditions.
    • A simplified method for obtaining the Pareto Law from Bose-Einstein statistics is presented.
    • The model is successfully applied to explain city size and growth phenomena.

    Conclusions:

    • The proposed stochastic process offers a unified framework for Bose-Einstein statistics and Gibrat's Law.
    • The derived Yule distribution provides an efficient route to the Pareto Law.
    • The application to city growth demonstrates the model's practical relevance in urban studies.